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LIBRARY

THE UNIVERSITY
OF CALIFORNIA

SANTA BARBARA

PRESENTED BY
PHILIP F. SIFF

^FIVE -PLACE

LOGARITHMIC AND TRIGONOMETRIC

TABLES

ARBANOBD BT

G. A. WENTWORTH, A.M.

G. A. HILL, A.M.

GINN & COMPANY

BOSTON . NEW YORK • CHICAGO • LONDON

,^o

Entered according to Act of Congress, in the year 1882, by

G. A. WENTWORTH and G. A. HILL
in thQ office of the Librarian of Congress at Waahington

Copyright. 1895, by G. A. Wentworth and G. A. Hill.
SU.1

(Cfje Stbencum \$re«K

GINN & COMPANY- PRO-
PRIETORS • BOSTON • U.S.A.

INTRODUCTION.

1. If the natural numbers are regarded as powers of ten, the
exponents of the powers are the Common or Briggs Logarithms of
the numbers. If A and B denote natural numbers, a and b their
logarithms, then 10" = A, 10* = £; or, written in logarithmic form,

log A = a, log B = b.

2. The logarithm of a product is found by adding the logarithms
of its factors.

For, Ax B = 10« X 106 = iQa + ft.

Therefore, log (^ x B) = a + b = logA + log B.

3. The logarithm of a quotient is found by subtracting the
logarithm of the divisor from that of the dividend.

Therefore, log — = a — b = log A — log B.

B

4. The logarithm of a power of a number is found by multiply-
ing the logarithm of the number by the exponent of the power.

For, J." = (lO")" = 10«».

Therefore, log A^= an= n log A.

5. The logarithm of the root of a number is found by dividing
the logarithm of the number by the index of the root.

For, y/A = -TlO" = 10»,

Therefore, log ^/A = - = -^ —

n n

6. The logarithms of 1, 10, 100, etc., and. of 0.1, 0.01, 0.001,
etc., are integral numbers. The logarithms of all other numbers
are fractions.

IT LOGAKITHMS.

10-1 = 0. 1, hence log 0.1 = - 1 •

10-2 = 0.01, hence log 0.01 = —2;

10-« = 0.001, hence log 0.001 = — 3 ;

and so on.

and

1.

1 and

2.

2 and

3.

and

-1.

For, 10° = 1, hence log 1 =

101 = 10, hence log 10 = 1

102 = 100, hence log 100 = 2
108 = 1000, hence log 1000 = 3

If the number is between 1 and 10, the logarithm is between

If the number is between 10 and 100, the logarithm is between

If the number is between 100 and 1000, the logarithm is between

If the number is between 1 and 0.1, the logarithm is between

If the number is between 0.1 and 0.01, the logarithm is between —1 and —2.

If the number is between 0.01 and 0.001, the logarithm is between —2 and —3,

And so on.

7. If the number is less than 1, the logarithm is negative (§ 6),
but is written in such a form that the fractional part is alwa.js positive.

For the number may be regarded as the product of two factors, one of
which lies between 1 and 10, and the other is a negative power of 10 ; the
logarithm will then take the form of a difference whose minuend is a positive
proper fraction, and whose subtrahend is a positive Lntegi-al number.

Thus, 0.48 = 4.8X0.1.

Therefore (§ 2), log 0.48 = log 4.8 + log 0.1 = 0.68124 - 1. (Page 1.)

Again, 0.0007 = 7 X 0.0001.

Therefore, log 0.0007 = log 7 + log 0.0001 = 0.84510 — 4.

The logarithm 0.84510 — 4 is often written 4.84510.

8. Every logarithm, therefore, consists of two parts : a positive
or negative integral number, which is called the Characteristic, and
a positive proper fraction, which is called the Mantissa.

Thus, in the logarithm 3.52179, the integral number 3 is the characteristic,
and the fraction .52179 the mantissa. In the logarithm 0.78254 — 2, the inte-
gral number — 2 is the characteristic, and the fraction 0.78254 is the mantissa.

9. If the logarithm is negative, it is customary to change the
form of the difference so that the subtrahend shall be 10 or a multiple
of 10. This is done by adding to both minuend and subtrahend a
number which will increase the subtrahend to 10 or a multiple of 10.

Thus, the logarithm 0.78254 — 2 is changed to 8.78254 — 10 by adding 8 to
both minuend and subtrahend. The logarithm 0.92737 — 13 is changed tc
7.92737 — 20 by adding 7 to both minuend and subtrahend.

10. The following rules are derived from § 6 : —

If the number is greater than 1, make the characteristic of the
logarithm one unit less than the number of figures on the left of
the decimal point.

If the number is less than 1, make the characteristic of the loga-
rithm negative, and one unit more than the number of zeros between
^e deeimal point and the first significant figure of the given number.

INTRODUCTION. ▼

If the characteristic of a given logarithm is positive, make the
number of figures in the integral part of the corresponding number
one more than the number of units in the characteristic.

If the characteristic is negative, make the number of zeros between
the decimal point and the first significant figure of the correspond-
ing number one less than the number of units in the characteristic.

Thus, the characteristic of log 7849.27 = 3 ;

the characteristic of log 0.037 = — 2 = 8.00000 — 10.
K the characteristic is 4, the corresponding number has five figures in its inte-
gral part. If the characteristic is — 3, that is, 7.00000 — 10, the corresponding
fraction has two zeros between the decimal point and the first significant figure.

11. The logarithms of numbers that can be derived one from
another by multiplication or division by an integral power of 10
have the same mantissa.

For, multiplying or dividing a number by an integral power of 10 will
increase or diminish its logarithm by the exponent of that power of 10 ; and
since this exponent is an integer, the mantissa of the logarithm will be
unaffected.

Thus, log 4.6021 =0.66296. (Page 9.)

log 460.21 = log (4.6021 X 102) = log 4.6021 + log lO^

= 0.66296 -f- 2 = 2.66296.
log 460210 = log (4.6021 X lO^) = log 4.6021 + log 10*

= 0.66296 -I- 5 = 5.66296.
log 0.046021 = log (4.6021 -f 102) = log 4.6021 - log 10»

= 0.66296 — 2 = 8.66296 — 10.

. TABLE I.

12. In this table (pp. 1-19) the vertical columns headed N con-
tain the numbers, and the other columns the logarithms. On page 1
both the characteristic and the mantissa are printed. On pages
2-19 the mantissa only is printed.

The fractional part of a logarithm can be expressed only approx-
imately, and in a five-place table all figures that follow the fifth are
rejected. Whenever the sixth figure is 5, or more, the fifth figure
is increased by 1. The figure 5 is written when the value of the
figure in the place in which it stands, together with the succeeding
^gures, is more than 4-^, but less than 5.

Thus, if the mantissa of a logarithm written to seven places is 5328732, it is
written in this table (a five-place table) 53287. If it is 5328751, it is written
63288. n it is 5328461 or 5328499, it is written in this table 6328S.

Again, if the mantissa is 6324981, it is written 53260 ; and if it is 4999967, it
is written fiOOOO.

■■<

VI LOGARITHMS.

This distinction between 5 and 5, in case it is desired to curtail
still further the mantissas of logarithms, removes all doubt whether
a 5 in the last given place, or in the last but one followed by a
zero, should be simply rejected, or whether the rejection should
lead us to increase the preceding figure by one unit.

Thus, the mantissa 13925 when reduced to four places should be 1392 ; but
13925 should be 1393.

To Find the Logarithm of a Given Number.

13. If the given number consists of one or two significant
figures, the logarithm is given on page 1. If zeros follow the sig-
nificant figures, or if the number is a proper decimal fraction, the
characteristic must be determined by § 10.

14. If the given number has three significant figures, it will be
found in the column headed N (pp. 2-19), and the mantissa of its
logarithm in the next column to the right, and on the same line.
Thus,

Page 2. log 145 = 2.16137, log 14500 = 4.16137.

Page 14. log 716 = 2.85491, log 0.716 = 9.85491 - 10.

15. If the given number has four significant figures, the first
three will be found in the column headed N, and the fourth at the
top of the page in the line containing the figures 1, 2, 3, etc. The
mantissa will be found in the column headed by the fourth figure,
and on the same line with the first three figures. Thus,

Page 15. log 7682 =3.88547, log 76.85 =1.88564.
Page 18. log 93280 = 4.96979, log 0.9468 = 9.97626 - 10.

16. If the given number has five or more significant figures, a
process called interpolation is required.

Interpolation is based on the assumption that between two con-
secutive mantissas of the table the change in the mantissa is directly
proportional to the change in the number.

Required the logarithm of 34237.

The required mantissa is (§ 11) the same as the mantissa for 3423.7 ; there-
fore it will be found by adding to the mantissa of 3423 seven-tenths of the
difference between the mantissas for 3423 and 3424.

The mantis.sa for 3423 is 53441.

The difference between the mantissas for 3423 and 3424 is 12.

Hence, the mantis.sa for 3423.7 is 53441 -|- (0.7 x 12) = 53449.

Therefore, the required logarithm of 34237 is 4.53449.

•

INTRODUCTIOir. TU

Required the logarithm of 0.0015764.

The required mantissa is the same as the mantissa for 1576.4 ; therefore
it will be found by adding to the mantissa for 1576 four-tenths of the difference
between the mantissas for 1576 and 1577.

The mantissa for 1576 is 19756.

The difference between the mantissas for 1576 and 1577 is 27.

Hence, the mantissa for 1576.4 is 19756 + (0.4 x 27) - 19767.

Therefore, the required logarithm of 0.0015764 is 7.19767 — 10.

Eequired the logarithm of 32.6708.

The required mantissa is the same as the mantissa for 3267.08 ; therefore
it will be found by adding to the mantissa for 3267 eight-hundredths of the
difference between the mantissas for 3267 and 3268.

The mantissa for 3267 is 51415.

The difference between the mantissas for 3267 and 3268 is 13.

Hence, the mantissa for 3267.08 is 51415 + (0.08 X 13) = 51416.

Therefore, the required logarithm of 32.6708 is 1.51416.

17. When the fraction of a unit in the part to be added to the
mantissa for four figures is less than 0.5 it is to be neglected ; when
it is 0.5 or more than 0.5 it is to be taken as one unit.

Thus, in the first example, the part to be added to the mantissa for 3423 is
8.4, and the .4 is rejected. In the second example, the part to be added to the
mantissa for 1576 is 10.8, and 11 is added.

To Find the Antilogarithm ; that is, the Number Corrb-

SPONDING TO A GiVEN LOGARITHM.

18. If the given mantissa can be found in the table, the first
three figures of the required number will be found in the same line
with the mantissa in the column headed N, and the fourth figure at
the top of the column containing the mantissa.

The position of the decimal point is determined by the charac-
teristic (§ 10).

Find the number corresponding to the logarithm 0.92002.

Page 16. The number for the mantissa 92002 is 8318.

The characteristic is ; therefore, the required number is 8.318.

Find the number corresponding to the logarithm 6.09167.

Page 2. The number for the mantissa 09167 is 1235.

The characteristic is 6 ; therefore, the required number is 1235000

Find the number corresponding to the logarithm 7.50825 — 10.

Page 6. The number for the mantissa 50325 is 3186.

The characteristic is — 3 ; therefore, the require'd number is 0.003186.

-^

van LOGARITHMS.

19. If the given mantissa cannot be found in the table, find
in the table the two adjacent mantissas between which the given
mantissa lies, and the four figures corresponding to the smaller of
these two mantissas will be the first four significant figures of the
required number. If more than four figures are desired, they may
be found by interpolation, as in the followiag examples :

Find the number corresponding to the logarithm 1.48762.

Here the two adjacent mantissas of the table, between which the given man-
tissa 48762 lies, are found to be (page 6) 48756 and 48770. The corresponding*
numbers are 3073 and 3074. The smaller of these, 3073, contains the first four
significant figures of the required number.

The difference between the two adjacent mantissas is 14, and the difference
between the corresponding numbers is 1.

The difference between the smaller of the two adjacent mantissas, 48756,
and the given mantissa, 48762, is 6. Therefore, the number to be annexed to
3073 is y\ of 1 = 0.428, and the fifth significant figure of the required number
is 4.

Hence, the required number is 30.734.

Find the number corresponding to the logarithm 7.82326 — 10.

The two adjacent mantissas between which 82326 lies are (page 13) 82321
"and 82328. The number corresponding to the mantissa 82321 is 6656.

The difference between the two adjacent mantissas is 7, and the difference
between the corresponding numbers is 1.

The difference between the smaller mantissa, 82321, and the given mantissa,
82326, is 5. Therefore, the number to be annexed to 6656 is f of 1 = 0.7, and
the fifth significant figure of the required number is 7.

Hence, the required number is 0.0066567.

In using a five-place table the numbers corresponding to man-
tissas may be carried to five significant figures, and in the first
part of the table to six figures.*

20. The logarithm of the reciprocal of a number is called the
Cologarithm of the number.

If A denotes any number, then

colog A = log — = log 1 — log ^ (§ 3) = — log A.

Hence, the cologarithm of a number is equal to the logarithm of
the number with the minus sign prefixed, which sign affects the
entire logarithm, both characteristic and mantissa.

*In most tables of logarithms proportional parts are given as an aid to
interpolation ; but, after a little practice, the operation can be performed nearly
as rapidly without them. Their omission allows a page with larger-faced type
and more open spacing, and consequently less trying to the eyes.

INTBODUCTIOir. IX

In order to avoid a negative mantissa in the cologarithm, it is
oustomary to substitute for — log A its equivalent

(10 — log ^) — 10.

Hence, the cologarithm of a number is found by subtracting the
logarithm of the number from 10, and then annexing — 10 to the
remainder.

The best way to perform the subtraction is to begin on the left
and subtract each figure of log A from 9 until we reach the last
significant figure, which must be subtracted from 10.

If log A is greater in absolute value than 10 and less than 20,
then in order to avoid a negative mantissa, it is necessary to write
— log A in the form

(20 — log ^)— 20.

So that, in this case, colog A is found by subtracting log A from
20, and then annexing — 20 to the remainder.

Find the cologarithm of 4007.

10 -10

Page 8. log 4007 = 3.60282

colog 4007= 6..39718 — 10

Find the cologarithm of 103992000000.

20 -20

Page 2. log 103992000000 = 11.01700

colog 103992000000 = 8.98300 — 20

If the characteristic of log A is negative, then the subtrahend,
— 10 or — 20, will vanish in finding the value of colog A.

Find the cologarithm of 0.004007.

10 ^ - 10

log 0.004007 = 7.66282 - 10
colog 0.004007 = 2.39718

With practice, the cologarithm of a number can be taken from
the table as rapidly as the logarithm itself.

By using cologarithms the inconvenience of subtracting the log-
arithm of a divisor is avoided. For dividing by a number is
equivalent to multiplying by its reciprocal. Hence, instead of
subtracting the logarithm of a divisor its cologarithm may be

liOGARITHMSl

EXEBCISES.

Find the logarithms of :

1. 6170.

4. 86.76.

7. 0.8694.

10.

67.3208.

2. 0.617.

5. 296.8.

8. 0.5908.

11.

18.5283.

3. 2867.

6. 7004.

9. 73243.

12.

0.0042003.

Find the cologarithms of :

13. 72433.

14. 802.376.

15. 15.7643.

16. 869.278.

17. 154000.

18. 70.0426.

19. 0.002403.

20. 0.000777.

21. 0.051828.

Find the antilogarithms of

22. 2.47246.

23. 7.89081.

24. 2.91221.

25. 1.26784.

26. 3.79029.

27. 5.18752.

28. 9.79029-10.

29. 7.62328 — 10.

30. 6.15466-10.

Computation by Logarithms.

21. (1) Find the value of x, if x = 72214 X 0.08203.

Page 14. log 72214 = 4.858G2

Page 16. log 0.08203 = 8.91897 — 10

By § 2. logx =3.77259

Page 11. z = 6923.63

(2) Find the value of x, if x = 5250 ^ 23487.

Page 10.
Page 4.
Page 4.

log 5250
colog 23487
logx
.-. X

= 3.72016
= 5.62917

10

= 9.34933 - 10 = log 0.22353
= 0.22353

(3) Find the value of x, ii x-

7.56 X 4667 X 567
899.1X0.00337X23435'

Page 15. log 7.56 = 0.87852

Page 9. log 4667 = 3.66904

Page 11. log 567 - 2.75368

Page 17. colog 899.1 = 7.04619 - 10

Page 6. colog 0.00337 '-- 2.47237

Page 4. colog 23436 = 5.63013-10
Page 5. log X

2.44983= log 281.73
281.73.

INTRODUCTION. XI

<'4) Find the cube of 376.

Page 7. log 376 = 2.57519

Multiply by 3 (§ 4), 3

Page 10. log 3763 = 7.72557 = log 53168600

.-. 3763 = 53158600.

. (5) Find the square of 0.003278.

Page 6. log 0.003278 = 7.51561-10

2

Page 2. log 0.0032782 = 15.03122 — 20 = log 0.000010745

.-.0.0032782= 0.000010745.

(6) Find the square root of 8322.

Page 16. log 8322 = 3.92023

Divide by 2 (§ 5), 2 )3.92023

log V8322 = 1.96012 = log 91.226

.-. V8322 = 91.226.

If the given number is a proper fraction, its logarithm will have
as a subtrahend 10 or a multiple of 10. In this case, before divid-
ing the logarithm by the index of the root, both the subtrahend and
the number preceding the mantissa should be increased by such a
number as will make the subtrahend, when divided by the index of
the root, 10 or a multiple of 10.

(7) Find the square root of 0.000043641.

Page 8. log 0.000043641 = 5.63989 — 10

10 - 10

Divide by 2 (§ 5), 2 )15.63989 — 20

Page 13. log V O. 000043641 = 7.81995 — 10 = log 0.0066062

.-. VO.000043641 = 0.0066062.

(8) Find the sixth root of 0.076553.

Page 15. log 0.076553 = 8.88397 - 10

50 -50

Divide by 6 (§ 5;, ^ 6 )58.88397-60

Page 13. log V'0. 076553 = 9.81400 - 10 => log 0-66163

.-. \/0.076553 = 0.65163.

Exercises.

Find by logarithms the value of :

45607 5.6123 2.667

31046' 0.01987* 0.05786"

XU LOGARITHMS,

0.06547

4.

6.

7.

8.

9.

10.

11.

12.

74.938 X 0.06938

4.667 X 0.03467
3.908 X 0.07189*

0.0075389 X 0.0079
0.00907 X 009784*

312 X 7.18 X 31.82
519 X 8.27 X 5.132*

0.007 X 57.83 X 28.18
9.317 X 00.28 X 476.5*

5.56 X 0.0007632 x 0.87654
2.79 X 0.0009524 X 1.46786 '

VI

003457 X 43.387 X 99.2 X 0.00026

005824 X 15.724 X 1.38 X 0.00089

8/ 23.815 X 29.36 X 0.007 X 0.62487
0.00072 X 9.236 X 5.924 X 3.0007'

V 3.1416 X 0.
1.7286 X 0.

031416 X 0.0031416

017285 X 0.0017285

TABLE n.

22. This table (page 20) contains the value of the number tt,
its most useful combinations, and their logarithms.

Find the length of an arc of 47° 32' 57'^ in a unit circle.

47° 32' 57" = 171177"

log 171177 - 5.23344

log \ = 4.68557 -

-10

log arc 47° 32' 57" = 9.91901 - 10 = log 0.82994
.-. length of arc = 0.82994.

Find the angle if the length of its arc in a unit circle = 0.54936.
log 0. 54936 = 9. 73986 - 10

oolog -r. = log a" = 5.31443
a

log angle = 6.05429 = log 113316

.-. angle = 113316" = 31° 28' 38".

INTBODUCTION. XOl

23. The relations between arcs and angles given in Table II.
are readily deduced from the circular measure of an angle.
In Circular Measure an angle is defined by the equation

arc

angle = —r^ — ,

in which the word arc denotes the length of the arc corresponding
to the angle, when both arc and radius are expressed in terms of
the same linear unit.

Since the arc and radius for a given angle in different circles
vary in the same ratio, the value of the angle given by this equa-
tion is independent of the value of the radius.

The angle which is measured by a radius-arc is called a Radian,
and is the angular unit in circular measure.

C i- C

Since C = 2 irB, it follows that — = 2 tt, and ^ = tt. Therefore,

Ji K

If the arc = circumference, the angle = 2 tt.

If the arc = semicircumference, the angle = tt.

If the arc = quadrant, the angle = -^ tt.

If the arc = radius, the angle = 1.

Therefore, tt = 180°, \it=^ 90°, -J tt = 60°, i tt = 45°, \ir = 30",
^ TT = 22^°, and so on.

Since 180° in common measure equals tt units in circular measure,

TT

1° in common measure = zr^r units in circular measure ;

loO

,.,.., 180°.

1 unit in circular measure = m common measure.

TT

By means of these two equations, the value of an angle expressed

in one measure may be changed to its value in the other measure.

Thus, the angle whose arc is equal to the radius is an angle of

180°
1 unit in circular measure, and is equal to , or 57° 17' 46",

TT

very nearly.

TABLE m.

24. This table (pp. 21-49) contains the logarithms of the trigo-
nometric functions of angles. In order to avoid nega,tive character-
istics, the characteristic of every logarithm is printed 10 too large.
Therefore, — 10 is to be annexed to each logarithm.

On pages 28^9 the characteristic remains the same throughout
each column, and is printed at the top and the bottom of the column.

ZIT LOGARITHMS.

But on pp. cJO, 49, the characteristic changes one unit in value at the
places marked with bars. Above these bars the proper characteristic
is printed at the top, and below them at the bottom, of the column.

25. On pages 28-49 the log sin, log tan, log cot, and log cos, of
1° to 89", are given to every minute. Conversely, this part of the
table gives the value of the angle to the nearest minute when
log sin, log tan, log cot, or log cos is known, provided log sin or
log cos lies between 8.24186 and 9.99993, and log tan or log cot
lies between 8.24192 and 11.75808.

If the exact value of the given logarithm of a function is not
found in the table, the value nearest to it is to be taken, unless
interpolation is employed as explained in § 26.

If the angle is less than 45° the number of degrees is printed at
the top of the page, and the number of minutes in the column to
the left of the columns containing the logarithm. If the angle
is greater than 45°, the number of degrees is printed at the bottom
of the page, and the number of minutes in the column to the right
of the columns containing the logarithms.

If the angle is less than 45°, the names of its functions are
printed at the top of the page ; if greater than 45°, at the bottom
of the page. Thus,

Page 38. log sin 21° 37' = 9.66631-10.

Page 45. log cot 36° 63' = 10. 12473 — 10 = 0. 1247^

Page 37. log cos 69° 14' = 9.64969-10.

Page 49. log tan 45° 59' = 10.01491 — 10 = 0.01491.

Page 48. If log cos = 9.87468 — 10, angle = 41° 28'.

Page 34. If log cot = 9.39353 — 10, angle = 76° 6'.

If log sin = 9.47760 — 10, the nearest log sin in the tahle is 9.47774 — 10
(page 36), and the angle corresponding to this value is 17° 29'.

If log tan = 0.76520 = 10.76520 — 10, the nearest log tan in the table is
10.76490 — 10 (page 32), and the angle corresponding to this value is 80° 15'.

26. If it is desired to obtain the logarithms of the functions of
angles that contain seconds, or to obtain the value of the angle in
degrees, minutes, and seconds, from the logarithms of its functions,
interpolation must be employed. Here it must be remembered
that.

The difference between two consecutive angles in the table
is 60".

Log sin and log tan increase as the angle increases ; log cos and
log cot diminish as the angle increases-

INTBODUCTION. XY

Find log tan 70° 46' 8",

Page 37. log tan 70° 46' = 0.45731.

The difference between the mantissas of log tan 70° 46' and log tan 70" 47'
ts 41, and ^^ of 41 = 5.

As the function is increasing, the 6 must be added to the figure in the fifth
place of the mantissa 45731 ; and

Therefore log tan 70° 46' 8" = 0.46736.

Find log cos 47° 35' 4".

Page 48. log cos 47° 35' = 9.82899 - 10.

The difference between this mantissa and the mantissas of the next log cos
is 14, and /^ of 14 = 1.

As the function is decreasing, the 1 must be subtracted from the figure in the
fifth place of the mantissa 82899 ; and

Therefore log cos 47° 35' 4" = 9.82898 — 10.

Find tlie angle for which log sin = 9.45359 — 10.

Page 35. The mantissa of the nearest smaller log sin in the table is 45334.

The angle corresponding to this value is 16° 30'.

The difference between 45334 and the given mantissa, 45359, is 25.

The difference between 45334 and the next following mantissa, 45377, is 43,
and If of 60" = 35".

As the function is increasing, the 35" must be added to 16° 30'; and the
required angle is 16° 30' 35".

Find the angle for which log cot = 0.73478.

Page 32. The mantissa of the nearest smaller log cot in the table is 73415.

The angle corresponding to this value is 10° 27'.

The difference between 73415 and the given mantissa is 63.

The difference between 73415 and the next following mantissa is 71, and f|
of 60" = 53".

As the function is decreasing, the 53" must be subtracted from 10° 27'; and
the required angle is 10° 26' 7".

Exercises.

Find

1. log sin 30° 8' 9". 9. log tan 25° 27' 47".

2. log sin 54° 54' 40". 10. log cos 56° 11' 57".

3. log cos 43° 32' 31". 11. log cot 62° 0' 4"
'4. log cos 69° 25' 11". 12. log cos 75° 26' 58*

5. log tan 32° 9' 17". 13. log tan 33° 27' 1?".

6. log tan 50° 2' 2". 14. log cot 81° 55' 24".

7. log cot 44° 33' 17". 16. log tan 89° 46' 36".

8. log cot 66° 9' 32". 16. log tan 1° 26' 66".

XVI

LOGARITHMS.

Find the angle A if

17.

log sin A = 9.70075.

26.

log cos A =

9 40008.

18.

logimJ.= 9.91289.

26.

log cot A —

9.78815.

19.

log cos ^= 9.86026.

27.

log cos A =

9.34301.

^0.

log cos ^= 9.64696.

28.

log tan A =

10.62288.

21.

log tan ^= 9.79840.

29.

log cot A =

9,66349.

22.

log tan^ = 10.07671.

30.

log sin vl =

8.39316.

23.

log cot A = 10.00676.

31.

log sin A =

8.06678.

24.

log cot ^= 9.84266.

32.

log tan A =

8.11148.

27. If log sec or log esc of an angle is desired, it may be found
from the table by the formulas,

sec A = 7 ; hence, log sec A = eolog cos A.

cos A

CSC A = — — r ; hence, log esc A = colog sin A.
sin A

Page 31. log sec 8° 28' = colog cos 8° 28' = 0.00476.
Page 42. log esc 69° 36' 44" = colog sin 69° 36' 44" = 0.06418.

28. If a given angle is between 0° and 1°, or between 89° and 90";
or, conversely, if a given log sin or log cos does not lie between the
limits 8.24186 and 9.99993 in the table; or, if a given log tan or
log cot does not lie between the limits 8.24192 and 11.75808 in the
table ; then pages 21-24 of Table III. must be used.

On page 21, log sin of angles between 0° and 0° 3', or log cos of
the complementary angles between 89° 57' and 90°, are given to
every second; for the angles between 0° and 0° 3', log tan = log sin,
and log cos = 0.00000 ; for the angles between 89° 57' and 90°,
log cot = log cos, and log sin = 0.00000.

On pages 22-24, log sin, log tan, and log cos of angles between
0° and 1°, or log cos, log cot, and log sin of the complementary
angles between 89° and 90°, are given to every 10".

Whenever log tan or log cot is not given, they may be found by
the formulas,

log tan = colog oot. log cot = colog tan.

Conversely, if a given log tan or log cot is not contained in the
table, then the colog must be found ; this will be the log cot .or
log tan, as the case may be, and will be contained in the table.

On pages 25-27 the logarithms of the functions of angles
between 1° and 2°, or between 88° and 90°, are given in the manner
employed on pages 22-24. These pages should be used if the angle
lies between these limits, and if not only degrees and minutes, but
degrees, minutes, and multiples of 10" are given or required.

INTKODUCTION. XVll

When the angle is between 0° and 2°, or 88° and 90°, and a
greater degree of accuracy is desired than that given by the table,
interpolation may be employed ; but for these angles interpolation
does not always give true results, and it is better to use Table IV.

Find log tan 0° 2' 47", and log cos 89° 37' 20".

Page 21. log tan 0° 2' 47" -- log sin 0° 2' 47" = 6.90829 — 10.
Page 23. log cos 89° 37' 20" = 7.81911 — 10.

Find log cot 0° 2' 15".

10 -10

Page 21. log tan 0° 2' 16" = 6.81591 — 10
Therefore, log cot 0° 2' 15" = 3.18409

Find log tan 89° 38' 30".

10 -10

Page 23. log cot 89° 38' 30" = 7.79617-10
Therefore, log tan 89° 38' 30" = 2.20383

Find the angle for which log tan = 6.92090 — 10.

Page 21. The nearest log tan is 6.92110 — 10.
The corresponding angle for which is 0° 2' 52".

Find the angle for which log cos = 7.70240 — 10.

Page 22. The nearest log cos is 7.70261 — 10.
I'he corresponding angle for which is 89° 42' 40".

Find the angle for which log cot = 2.37368.

This log cot is not contained in the table.
The colog cot = 7.62632 — 10 = log tan.

The log tan in the table nearest to this is (page 22) 7.62510— 10, and the
angle corresponding to this value of log tan is 0° 14' 30".

29. If an angle x is between 90° and 360°, it follows, from
formulas established in Trigonometry, that,

between 90° and 180°, between 180° and 270°,

log sin x = log sin (180° — x), log sin x = log sin {x — 180°)„,

log cos X = log cos (180° — a;)„, log cos x = log cos {x — 180°)„;

liog tan X = log tan (180° — a;)„, log tan x = log tan (x — 180°),

log cot X = log cot (180° — x)„ ; log cot x = log cot (x — 180°) j

between 270° and 360°,
log sin X = log sin (360° — x)„,
log cos cc = log cos (360° — x),
log tan X = log tan (360° — x)„,
log cot x = log cot (360° — aj)„.

XTlll LOGARITHMS.

The letter n is placed (according to custom) after the logarithms
of those functions which are negative in value.

The above formulas show, without further explanation, how to
find by means of Table III. the logarithms of the functions of any
angle between 90° and 360°.

Thus, log sin 137° 45' 22" = log sin 42° 14' 38" = 9.82756 — 10.
log cos 137° 45' 22" = log„ cos 42° 14' 38" = 9.86940„ — 10.
log tan 137° 45' 22" = log„ tan 42° 14' 38" = 9.95815„ — 10.
log cot 137° 45' 22" = log„ cot 42° 14' 38" = 0.04185„.
log sin 209° 32' 50" = log„ sin 29° 32' 50" = 9.69297„ — 10.
log cos 330° 27' 10" = log cos 29° 32' 50" = 9.93949 — 10.

Conversely, to a given logarithm of a trigonometric function
there correspond between 0° and 360° four angles, one angle in
each quadrant, and so related that if x denote the acute angle, the
other three angles are 180°— cc, 180° + a;, and 360° — a;.

If besides the given logarithm it is known whether the function
is positive or negative, the ambiguity is confined to two quadrants,
therefore to two angles.

Thus, if the log tan = 9.47451 — 10, the angles are 16° 36' 17" in Quadrant I.
and 196° 36' 17" in Quadrant III. ; but if the log tan = 9.47451„— 10, the angles
are 163° 23' 43" in Quadrant II. and 343° 23' 43" in Quadrant IV.

To remove all ambiguity, further conditions are required, or a
knowledge of the special circumstances connected with the problem
in question.

TABLE IV.

30. This table (page 50) must be used when great accuracy is
desired in working with angles between 0° and 2°, or between 88°
and 90°.

The values of S and T are such that when the angle a is
expressed in seconds,

S = log sin a — log a",
T = log tan a — log a".

Hence follow the formulas given on page 50.

The values of S and T are printed with the characteristic 10 too
large, and in using them — 10 must always be annexed.

Find log sin 0° 58' 17".

0° 58' 17" = 3497"
log 3497 = 3.54370

S = 4.68555 — 10
log sin 0° 58' 17" = 8.22926 - 10

Find log cos 88° 26' 41.2".

90° - 88° 26' 41.2" = )° 33' 18.8"
= 5598.8"
log 6598.8 = 3.74809

S = 4.68652 - 10
log cos 88* 26' 41.2" = 8.43361 - 10

INTRODUCTION. XIX

Find log tan 0° 52' 47.5".

0° 52' 47.5" = 3167.5"
log 3167.5 = 3.60072

T = 4.68561 - 10
log tan 0° 52' 47.5" = 8.18633 - 10

Find log tan 89" 54' 37.362".

90° — 89° 54' 37.362" = 0° 5' 22.638"
= 322.638"
log 322.638 = 2.50871

T = 4.68558 — 10
log cot 89° 54' 37.362" = 7.19429 - 10
log tan 89° 54' 37.362" = 2.80571

Find the angle, if log sin = 6.72306 — 10.

6.72306-10
S = 4.68557 — 10
Subtract, 2.03749 = log 109.016

109.015" = 0° 1' 49.016".

Find the angle for which log cot = 1.67604.

cologcot = 8.32396 — 10
T = 4.68564 - 10
Subtract, 3.63832 = log 4-348.3

4348.3" = 1° 12' 28.3".

Find the angle for which log tan = 1.55407.

colog tan = 8.44593 — 10
T = 4.68 569— 10
Subtract, 3.76024 = log 5757.6

5767.6" = 1° 35' 57.6",

and 90° -1° 35' 67.6" = 88° 24' 2.4".
Therefore, the angle required is 88° 24' 2.4".

TABLE V.

31. This table (p. 51), containing the circumferences and areas
of circles, does not require explanation.

TABLE VI.

32. Table VI. (pp. 52-69) contains the natural sines, cosines,
tangents, and cotangents of angles from 0° to 90°, at inter-
vals of 1'. If greater accuracy is desired it may be obtained
by interpolation.

Note. In preparing the preceding explanations, we have made free use
of the Logarithmic Tables by F. G. Gauss. For Table VI. we are indebted
to D. Carhart.

TABLE VII.

33. This table (pp. 70-75) gives the latitude and departure to
three places of decimals for distances from 1 to 10, corresponding
to bearings from 0° to 90° at intervals of 15'.

XX

LOGARITHMS.

If the bearing does not exceed 45° it is found in the left-haxid
column, and the designations of the columns under "Distance"
are taken from the top of the page ; but if the bearing exceeds
45°, it is found in the ri^A^-hand column, and the designations
of the columns under " Distance " are taken from the bottom of
the page.

The method of using the table will be made plain by the follow-
ing examples : —

(1) Let it be required to find the latitude and departure of the
course N. 35° 15' E. 6 chains.

On p. 76, left-hand column, look for 35° 15' ; opposite this bearing, in the
vertical column headed "Distance 6," are found 4.900 and 3.463 under the
headings "Latitude" and "Departure" respectively. Hence, latitude or
northing = 4.900 chains, and departure or easting = 3.463 chains.

(2) Let it be required to find the latitude and departure of the
course S. 87° W. 2 chains.

As the bearing exceeds 45°, we look in the right-hand column of p. 70, and
opposite 87° in the column marked " Distance 2 " we find (taking the designa-
tions of the columns from the bottom of the page) latitude = 0.105 chains, and
departure = 1.997 chains. Hence, latitude or southing = 0. 105 chains, and
departure or westing = 1.997 chains.

(3) Let it be required to find the latitude and departure of the
course N. 15° 45' W. 27.36 chains.

In this case we find the required numbers for each figure of the distance
separately, arranging the work as in the following table. In practice, only the
last columns under " Latitude " and " Departure " are written.

DlSTAJfCB.

Latitude.

Departure.

20 = 2 X 10

7

0.3 =3-rl0
0.06 = 6 ^ 100

1.925 X 10 = 19.25

6.737

2.887 -=-10 =0.289

6.776^100 = 0.058

0.543 X 10 = 5.43
1.90
0.814 -r 10 =0.081
1.628 -r- 100 = 0.016

27.36

26.334

7.427

Heaoe, latitude = 26.334 chains, and departure = 7.427 ohaiiu.

riBLE L

THB

col

Imon oe beiggs logaeithms

•

OF THE

:n"atueal numbers

From 1 to 10000.

•^ ,_ *.

- ':>

'-7

1-100

N log

N

log

N log

N

log

N

log

1 0.00 000

21

1.32 222

41 1. 61 278

61

1. 78 533

81

1.90 849

2 0.30103

22

1. 34 242

42 1. 62 325

62

1. 79 239

82

1. 91 381

3 0.47 712

23

1. 36 173

43 1.63 347

63

1. 79 934

83

1. 91 908

4 0.60 206

24

1.38 021

44 1. 64 345

64

1.80 618

84.

1.92 428

5 0.69 897

25

1. 39 794

45 1. 65 321

65

1. 81 291

85

1. 92 942

6 0.77 815

26

1.41497

46 1.66 276

66

1. 81 954

86

1. 93 4i0

7 0.84 510

27

1. 43 136

47 1.67 210

67

1. 82 607

87

1. 93 952

8 0.90309

28

1. 44 716

48 1. 68 124

68

1. 83 251

88

1.94 448

9 0.95 424

29

1.46 240

49 1.69 020

69

1. 83 885

89

1.94 939

10 1.00 000

30

1.47 712

50 1.69 897

70

1. 84 510

90

1. 95 424

11 1.04139

31

1. 49 136

51 1.70 757

71

1. 85 126

91

1.95 904

12 1.07 918

32

1.50 515

52 1.71600

72

1. 85 733

92

1.96 379

13 1.11394

33

1. 51 851

53 1.72 428

73

1. 86 332

93

1. 96 848

14 1. 14 613

34

1. 53 148

54 1. 73 239

74

1.86 923

94

1.97 313

15 1.17 609

35

1. 54 407

55 1.74 036

75

1.87 506

95

1. 97 772

16 1.20 412

36

1.55 630

56 1.74 819

76

1. 88 081

96

1. 98 227

17 1.23 045

37

1. 56 820

57 1. 75 587

77

1.88 649

97

1.98 677

18 1. 25 527

38

1.57 978

58 1.76 343

78

1. 89 209

98

1. 99 123

19 1.27 875

39

1. 59 106

59 1. 77 085

79

1. 89 763

99

1.99 564

20 1.30103

40

1.60 206

60 1.77 815

80

1.90 309

100

2.00000

N log

N

log

N log

N

log

N

log

I- 100

2

100-150

N

1

2

3

4

5

6

7

8

9

lOO

00 000

00043

00 087

00130

00173

00 217

00 260

00 303

00 346

00 389

101

00 432

00 475

00 518

00 561

00 604

00 647

00 689

00 732

00 775

00 817

102

00 860

00 903

00 945

00 988

01030

01072

0ill5

01157

01199

01242

103

01284

01326

01368

01410

01452

01494

01536

01578

01620

01662

10+

01703

01745

01787

01828

01870

01912

01953

01995

02 036

02 078

105

02 119

02160

02 202

02 243

02 284

02 325

02 366

02 407

02 449

02 490

106

02 531

02 572

02 612

02 653

02 694

02 735

02 776

02 816

02 857

02 898

107

02 938

022Z9_03019-^03 060

03 100

03 141

03 181

03 222

03 262

03 302

108

03 342

03 383

03 423

03 463

03 503

03 543

03 583

03 623

03 663

03 703

109

03 743

03 782

03 822

03 862

03 902

03^941

03 981

04 021

04 060

04100

110

04139

04179

04 218

04 258

04 297

04 336

04 376

04 415

04 454

04 493

111

04 532

04 571

04 610

04 650

04 689

04 727

04 766

04 80^

1^4 844

04 883

112

04 922

04 961

04 999

05 038

05 077

05 115

05 154

05 19lP5 231

05 269

113

05 308

05 346

05 385

05 423

05 461

05 500

05 538

05 576

05 614

05 652

114

05 690

05 729

05 767

05 805

05 843

05 881

05 918

05 956

05 994

06 032

115

06 070

06108

06145

06183

06 221

06 258

06 296

06 333

06 371

05408

116

06 446

06 483

06 521

06 558

06 595

06 633

06 670

06 707

06 744

06 781

117

06 819

06 856

06 893

06 930

06 967

07 004

07 041

07 078

07115

07151

118

07188

07 225

07 262

07 298

07 335

07 372

07 408

07 445

07 482

07 518

119

07 55i

07 591

07 628

07 664

07 700

07 737

07 773

07 809

07 846

07 882

120

07 918

07 954

07 990

08 027

08 063

08 099

08135

08171

08 207

08 243

121

08 279

08 314

08 350

08 386

08 422

08 458

08 493

08 529

08 565

08 600

122

08 636

08 672

08 707

08 743

08 778

08 814

08 849

08 884

08 920

08 955

123

08991

09 026

09 061

09 096

09132

09167

09 202

09 237

09 272

09 307

124

09 342

09 377

09 412

09 447

09 482

09 517

09 552

09 587

09 621

09 65^

125

09 691

09 726

09 760

09 795

09 830

09 864

09 899

09 934

09 968

10 003

126

10 037

10 072

10106

10140

10175

10 209

10 243

10 278

10 312

10 346

127

10380

10415

10449

10 483

10 517

10 551

10 585

10 619

10 653

10 687

128

10 721

10 751

10 789

10 823

10 857

10 890

10 924

10 958

10 992

11025

129

11 059

11093

11126

11160

11193

11227

11261

11294

11327

11361

130

11394

11428

11461

11494

11528

11561

11594

11628

11661

11694

131

11727

11760

11793

11826

11860

11893

11926

11959

11992

12 024

132

12 057

12 090

12123

12156

12189

12 222

12 254

12 287

12 320

12 352

133

12 385

12 418

12 450

12 483

12 516

12 548

12 581

12 613

12 646

12 678

134

12 710

12 743

12 775

12 808

12 840

12 872

12 905

12 937

12 969

13 001

135

13 033

13 066

13 098

13 130

13 162

13 194

13 226

13 258

13 290

13 322

136

13 354

13 386

13 418

13 450

13 481

13 513

13 545

13 577

13 609

13 640

137

13 672

13 704

13 735

13 767

13 799

13 830

13 862

13 893

13 925

13 956

138

13 988

14 019

14 051

14 082

14114

14145

14176

14 208

14 239

14 270

139

14 301

14 333

14 364

14 395

14 426

14 457

14 489

14 520

14 551

14 582

140

14 613

14 644

14 675

14 706

14 737

14 768

14 799- 14 829

14 860

14 891

141

14 922

14 953

14 983

15 014

15 045

15 076

15 106

15 137

15 168

15 198

142

15 229

15 259

15 290

15 320

15 351

15 381

15 412

15 442

15 473

15 503

143

15 534

15 564

15 594

15 625

15 655

15 685

15 715

15 746

15 776

15 806

144

15 836

15 866

15 897

15 927

15 957

15 987

16 017

16 047

16 077

16107

145

16137

16167

16197

16 227

16 256

16 286

16316

16 346

16 376

16 406

146

16435

16 465

16495

16 524

16 554

16 584

16 613

16 643

16 673

16 702

147

16 732

16 761

16 791

16 820

16 850

16 879

16909

16 938

16 967

16 997

148

17026

17 056

17 085

17114

17143

17173

17 202

17 231

17 260

17 289

149

17 319

17 348

17 377

17 406

17 435

17 464

17 493

17 522

17 551

17 580

150

17 609

17 638

17 667

17 696

17 725

17 754

17 782

17 811

17 840

17 869

N

O

1

2

3

4

5

6

7

8

9

100-150

150-200

8

N

1 .

2 3

4

5

17 754

6 7

8

9

150

17 609

17 638

17 667 17 696

17 725

17 782 17 811

17 840

17 869

•151

17 898

17 926

17 955 17 984

18 013

18 041

18 070 18 099

18127

18156

152

18184

18 213

18 241 18 270

18 298^

18 327

18 355 18 384

18 412

18 441

153

18469

18 498

18 526 18 554

18 583

18 611

18 639 18 667

18 696

18 724

154

18 752

18 780

18 808 18 837

18 865

18 893

18 921 18949

18 977

19 005

165

19 033

19 061

19 089 19117

19145

19173

19 201 19 229

19 257

19 285

156

19 312

19 340

19 368 19 396

19 424

19 451

19 479 19 507

19 535

19 562

157

19 590

19 618

19 645 19 673

19 700

19 728

19 756 19 783

19 811

19 838

158

19 866

19 893

19 921 19 948

19 976

20 003

20 030 20 058

20 085

20112

159

20140

20167

20194 20 222

20 249

20 276

20 303 20 330

20 358

20 385

160

20 412

20 439

20466 20 493

20 520

20 548

20 575 20 602

20 629

20 656

161

20 683

20 710

20 737 20 763

20 790

20 817

20 844 20 871

20 898

20 925

162

20 952

20 978

21005 21032

21059

21085

21112 21139

21165

21192

163

21219

21245

21272 21299

21325

21352

21378 21405

21431

21458

164

21484

21511

21537 21564

21590

21617

21643 21669

21696

21722

165

21748

2177i

21801 21827

21854

21880

21906 21932

21958

21985

166

22 011

22 037

22 063 22 089

22 115

22 141

22167 22 194

22 220

22 246

167

22 272

22 298

22 324 22 350

22 376

22 401

22 427 22 453

22 479

22 505

168

22 531

22 557

22 583 22 608

22 634

22 660

22 686 22 712

22 737

22 763

169

22 789

22 814

22 840 22 866

22 891

22 917

22 943 22 968

22 994

23 019

170

23 045

23 070

23 096 23121

23 147

23172

23 198 23 223

23 249

23 274

171

23 300

23 325

23 350 23 376

23 401

23 426

23 452 23 477

23 502

23 528

172

23 553

23 578

23 603 23 629

23 654

23 679

23 704 23 729

23 754

23 779

173

23 805

23 830

23 855 23 880

23 905

23 930

23 955 23 980

24 005

24 030

174

24 05i

24 080

24105 24130

24155

24 180

24 204 24 229

24 254

24 279

175

24 304

24 329

24 353 24 378

24 403

24 428

24 452 24 477

24 502

24 527

176

24 551

24 576

24 601 24 625

24 650

24 674

24 699 24 724

24 748

24 773

177

24 797

24 822

24 846 24 871

24 895

24 920

24 944 24 969

24 993

25 018

178

25 042

25 066

25 091 25 115

25 139

25 164

25 188 25 212

25 237

25 261

179

25 285

25 310

25 334 25 358

25 382

25 406

25 431 25 455

25 479

25 503

180

25 527

25 551

25 575 25 600

25 624

25 648

25 672 25 696

25 720

25 744

181

25 768

25 792

25 816 25 840

25 864

25 888

25 912 25 935

25 959

25 983

182

26007

26 031

26 055 26 079

26102

26126

26150 26174

26198

26 221

183

26 245

26 269

26 293 26 316

26 340

26 364

26 387 26 411

26 435

26 458

184

26 482

26 505

26 529 26 553

26 576

26 600

26 623 26 647

26 670

26 694

185

26 717

26 741

26 764 26 788

26 811

26 834

26 858 26 881

26 905

26 928

186

26 951

26 975

26 998 27 021

27 045

27 068

27 091 27114

27138

27 161

187

27184

27 207

27 231 27 254

27 277

27 300

27 323 27 346

27 370

27 393

188

27 416

27 439

27 462 27 485

27 508

27 531

27 554 27 577

27 600

27 623

189

27 646

27 669

27 692 27 715

27 738

27 761

27 784 27 807

27 830

27 852

190

27 875

27 898

27 921 27 944

27 967

27 989

28 012 28 035

28 058

28 081

191

28103

28126

28149 28171

28 194

28 217

28 240 28 262

28 285

28 307

192

28 330

28 353

28 375 28 398

28 421

28443

28 466 28 488

28 511

28 533

193

28 556

28 578

28 601 28 623

28 646

28 668

28 691 28 713

28 735

28 758

194

28 780

28 803

28 825 28 847

28 870

28 892

28 914 28 937

28 959

28 981

195

29 003

29 026

29 04.3 4/ 70

29 092

29115

29137 29159

29 181

29 203

196

29 226

29 248

29 270 29'292

29 314

29 336

29 358 29 380

29 403

29 425

197

29 447

29 469

29 491 29 513

29 535

29 557

29 579 29 601

29 623

29 645

198

29 667

29 688

29 710 29 732

29 754

29 776

29 798 29 820

29 842

29 863

199

29 885

29 907

29 929 29 951

29 973

29 994

30 016 30 038

30 060

30 081

200

30103

3012i

30146 30168

30190

30 211

30 233 30 255

30 276

30 298

N

1

2 3

4

5

6 7

8

9

150-200

4

200-250

N

O

1 2

3

4

5 6

7

8

9

200

30103

30125 30146

30168

30190

30 211 30 233

30 255

30 276

30 298

201

30320

30 341 30 363

30384

30406

30 428 30449

30 471

30 492

30 514

202

30 535

30 557 30 578

30 600

30 621

30 643 30 664

30 685

30 707

30 728

203

30 750

30 771 30 792

30 814

30 835

30 856 30 878

30 899

30 920

30 942

20+

30 963

30984 31006

31027

31048

31069 31091

31112

31133

31154

205

31175

31197 31218

31239

31260

31281 31302

31323

31345

31366

206

31387

31408 31429

31450

31471

31492 31513

31534

31555

31576

207

31597

31618 31639

31660

31681

31702 31723

31744

31765

31785

208

31806

31827 31848

31869

31890

31911 31931

31952

31973

31994

209

32 015

32 035 32 056

32 077

32 098

32 118 32 139

32 160

32181

32 201

210

32 222

32 243 32 263

32 284

32 305

32 325 32 346

32 366

32 387

32 408

211

32 428

32 449 32 469

32 490

32 510

32 531 32 552

32 572

32 593

32 613

212

32 634

32 654 32 675

32 695

32 715

32 736 32 756

32 777

32 797

32 818

213

32 838

32 858 32 879

32 899

32 919

32 940 32 960

32 980

33 001

33 021

214

33 041

33 062 33 082

33 102

33 122

33 143 33 163

33 183

33 203

33 224

215

33 244

33 264 33 284

33 304

33 325

33 345 33 365

33 385

33 405

33 425

216

33 445

33 465 33 486

33 506

33 526

33 546 33 566

33 586

33 606

33 626

217

33 646

33 666 33 686

33 706

33 726

33 746 33 766

33 786

33 806

33 826

218

33 846

33 866 33 885

33 905

33 925

33 945 33 965

33 985

34 005

34 025

219

34 044

34 064 34 084

34104

34 124

34 143 34163

34183

34 203

34 223

220

34 242

34 262 34 282

34 301

34 321

34 341 34 361

34 380

34 400

34 420

221

34 439

34 459 34 479

34 498

34 518

34 537 34 557

34 577

34 596

34 616

222

34 635

34 655 34 674

34 694

34 713

34 733 34 753

34 772

34 792

34 811

223

34 830

34 850 34 869

34 889

34 908

34 928 34 947

34 967

34 986

35 005

224

35 025

35 044 35 064

35 083

35102

35 122 35 141

35 160

35 180

35 199

, 225

35 218

35 238 35 257

35 276

35 295

35 315 35 334

35 353

35 372

35 392

226

35 411

35 430 35 449

35 468

35 488

35 507 35 526

35 545

35 564

35 583

227

35 603

35 622 35 641

35 660

35 679

35 698 35 717

35 736

35 755

35 774

228

35 793

35 813 35 832

35 851

35 870

35 889 35 908

35 927

35 946

35 965

229

35 984

36 003 36021

36040

36 059

36 078 36097

36116

36135

36154

230

36173

36192 36 211

36 229

36 248

36 267 36 286

36 305

36 324

36 342

231

36 361

36 380 36 399

36 418

36 436

36 455 36 474

36 493

36 511

36 530

232

36 549

36 568 36 586

36 605

36 624

36 642 36 661

36 680

36 698

36 717

233

36 736

36 754 36 773

36 791

36 810

36 829 36 847

36 866

36 884

36 903

234

36922

36 940 36959

36 977

36 996

37 014 37 033

37 051

37 070

37 088

235

37107

37125 37144

37162

37181

37199 37 218

37 236

37 254

37 273

236

37 291

37 310 37 328

37 346

37 365

37 383 37 401

37 420

37 438

37 457

237

37 475

37 493 37 511

37 530

37 548

37 566 37 585

37 603

37 621

37 639

238

37 658

37 676 37 694

37 712

37 731

37 749 37 767

37 785

37 803

37 822

239

37 840

37 858 37 876

37 894

37 912

37 931 37 949

37 967

37 985

38 003

240

38 021

38 039 38057

38075

38 093

38112 38130

38 148

38166

38184

241

38 202

38 220 38 238

38 256

38 274

38 292 38 310

38 328

38 346

38 364

242

38 382

38 399 38 417

38 435

38 453

38 471 38 489

38 507

38 525

38 543

243

38 561

38 578 38 596

38 614

38 632

38 650 38 668

38 686

38 703

38 721

244

38 739

38 757 38 775

38 792

38 810

38 828 38 846

38 863

38 881

38 899

245

38917

38 934 38 952

38970

38 987

39 626^39 023

39 041

39 058

39 076

246

39 094

39111 39129

39 146

39164

39182 39199

39 217

39 235

39 252

247

39 270

39 287 39 305

39 322

39 340

39 358 39 375

39 393

39 410

39 428

248

39445

39 463 39 480

39 498

39 515

39 533 39 550

39 568

39 585

39 602

249

39 620

39 637 39 655

39 672

39 690

39 707 39 724

39 742

39 759

39 777

250

39 794

39 811 39 829

39 846

39 863

39 881 39 898

39 915

39933

39 950

N

O

1 2

3

4

5 6

7

8

9

200-260

250-300

N

O

1

2 3 4

6

6

7 8

9

260

39 794

39 811

39 829 39 846 39 863

39 881

39 898

39 915 39 933

39 950

251

39 967

39 985

40 002 40 0.19 40 037

40 054

40 071

40088 40106

40123

252

40140

40157

40175 40 192 40 209

40 226

40 243

40 261 40 278

40 295

253

40 312

40 329

40 346 40 364 40 381

40 398

40415

40 432 40 449

40466

254

40 483

40 500

40 518 40 535 40 552

40 569

40 586

40 603 40 620

40 637

256

40 654

40 671

40 688 40 705 40 722

40 739

40 756

40 773 40 790

40807

256

40 824

40 841

40 858 40 875 40 892

40 909

40 926

40943 40960

40976

257

40 993

41010

41027 41044 41061

41078

41095

41 111 41 128

41 145

258

41 162

41179

41 196 41 212 41 229

41246

41263

41 280 41 296

41313

259

41330

41347

41363 41380 41397

41414

41430

41447 41464

41481

260

41497

41514

41531 41547 41564

41581

41597

41614 41631

41647

261

41664

41681

41697 41714 41731

41747

41764

41 780 41 797

41814

262

41830

41847

41863 41880 41896

41913

41929

41946 41 %3

41979

263

41996

42 012

42 029 42 045 42 062

42 078

42 095

42 111 42 127

42144

26+

42 160

42 177

42 193 42 210 42 226

42 243

42 259

42 275 42 292

42 306

265

42 325

42 341

42 357 42 374 42 390

42 406

42 423

42 439 42 455

42 472

266

42 4SS

42 504

42 521 42 537 42 553

42 570

42 586

42 602 42 619

42 635

267

42 651

42 667

42 684 42 700 42 716

42 732

42 749

42 765 42 781

42 797

268

42 813

42 830

42 846 42 862 42 878

42 894

42 911

42 927 42 943

42 959

269

42 975

42 991

43 008 43 024 43 040

43 056

43 072

43 088 43 104

43 120

270

43136

43 152

43 169 43 185 43 201

43 217

43 233

43 249 43 265

43 281

271

43 297

43 313

43 329 43 345 43 361

43 377

43 393

43 409 43 425

43 441

272

43 457

43 473

43 489 43 505 43 521

43 537

43 553

43 569 43 584

43 600

273

43 616

43 632

43 648 43 664 43 680

43 696

43 712

43 727 43 743

43 759

294

43 775

43 791

43 807 43 823 43 838

43 854

43 870

43 886 43 902

43 917

275

43 933

43 949

43 965 43 981 43 996

44 012

44 028

44 044 44 059

44 075

276

44 091

44 107

44 122 44 138 44 154

44170

44 185

44 201 44 217

44 232

277

44 248

44 264

44 279 44 295 44 311

44 326

44 342

44 358 44 373

44 389

278

44 404

44 420

44 436 44 451 44 467

44 483

44 498

44 514 44 529

44 545

279

44 560

44 576

44 592 44 607 44 623

44 638

44 654

44 669 44 685

44 700

280

44 716

44 731

44 747 44 762 44 778

44 793

44 809

44 824 44 840

44 855

281

44 871

44 886

44 902 44 917 44 932

44 948

44 963

44 979 44 994

45 010

282

45 025

45 040

45 056 45 071 45 086

45 102

45 117

45 133 45 148

45 163

283

45 179

45 194

45 209 45 225 45 240

45 255

45 271

45 286 45 301

45 317

284

45 332

45 347

45 362 45 378 45 393

45 408

45 423

45 439 45 454

45 469

285

45 484

45 500

45 515 45 530 45 545

45 561

45 576

45 591 45 606

45 621

286

45 637

45 652

45 667 45 682 45 697

45 712

45 728

45 743 45 758

45 773

287

45 788

45 803

45 818 45 834 45 849

45 864

45 879

45 894 45 909

45 924

288

45 939

45 954

45 969 45 984 46 000

46015

46 030

46 045 46 060

46 075

289

46 090

46105

46120 46135.46 150

46165

46180

46195 46 210

46 225

290

46 240

46 255

46 270 46 285 46 300

46 315

46 330

46 345 46 359

46 374

291

46 389

46 404

46 419 46 434 46 449

46 464

46 479

46 494 46 509

46 523

292

46 538

46 553

46 568 46 583 46 598

46 613

46 627

46 642 46 657

46 672

293

46 687

46 702

46 716 46 731 46 746

46 761

46 776

46 790 46 805

46 820

294

46 83i

46 850

46 864 46 879 46 894

46 909

46 923

46 938 46 953

46 967

295

46982

46 997

47 012 47 026 47 041

47 056

47 070

47 085 47 100

47114

296

47129

47 144

47 159 47 173 47 188

47 202

47 217

47 232 47 246

47 261

297

47 276

47 290

47 305 47 319 47 334

47 349

47 363

47 378 47 392

47 407

298

47 422

47 436

47 451 47 465 47 480

47 494

47 509

47 524 47 538

47 553

299

47 567

47 582

47 596 47 611 47 625

47 640

47 654

47 669 47 683

47 698

300

47 712

47 727

47 741 47 756 47 770

47 784

47 799

47 813 47 828

47 842

N

O

1

2 3 4

5

6

7 8

9

250-300

300-350

N

o

1

2

3

4

5

6

7

8

O

300

47 712

47 727

47 741

47 756

47 770

47 784

47 799

47 813

47 828

47 842

301

47 857

47 871

47 885

47 900

47 914

47 929

47 943

47 958

47 972

47 986

302

48001

48 015

48 029

48 044

48 058

48 073

48 087

48101

48116

48130

303

48144

48 159

48173

48187

48 202

48 216

48 230

48 244

48 259

48 273

304

48 287

48 302

48 316

48 330

48 344

48 359

48 373

48 387

48 401

48 416

305

48 430

48 444

48 458

48 473

48 487

48 501

48 515

48 530

48 544

48 558

306

48 572

48 586

48 601

48 615

48 629

48 643

48 657

48 671

48 686

48 700

307

48 714

48 728

48 742

48 756

48 770

48 785

48 799

48 813

48 827

48 841

308

48 855

48 869

48 883

48 897

48 911

48 926

48 940

48 954

48 968

48 982

309

48 996

49 010

49 024

49 038

49 052

49066

49 080

49 094

49108

49122

310

49136

49150

49 164

49178

49192

49 206

49 220

49 234

49 248

49 262

311

49 276

49 290

49 304

49 318

49 332

49 346

49 360

49 374

49 388

49 402

312

49 415

49 429

49 443

49 457

49 471

49 485

49 499

49 513

49 527

49 541

313

49 554

49 568

49 582

49 596

49 610

49 624

49 638

49 651

49 665

49 679

31+

49 693

49 707

49 721

49 734

49 748

49 762

49 776

49 790

49 803

49 817

315

49 831

49 845

49 859

49 872

49 886

49 900

49 914

49 927

49 941

49 955

316

49 969

49 982

49 996

50 010

50 024

50 037

50 051

50 065

50 079

50 092

317

50106

50120

50133

50147

50161

50174

50188

50 202

50 215

50 229

318

50 243

50 256

50 270

50 284

50 297

50 311

50 325

50 338

50 352

50 365

319

50379

50393

50 406

50420

50 433

50 447

50 461

50 474

50 488

50 501

320

50 515

50 529

50 542

50 556

50 569

50 583

50 596

50 610

50 623

50 637

321

50 651

50 664

50 678

50 691

50 705

50 718

50 732

50 745

50 759

50 772

322

50 786

50 799

50 813

50 826

50 840

50 853

50 866

50 880

50 893

50 907

323

50 920

50 934

50 947

50 961

50 974

50 987

51001

51014

51028

51041

324

5105i

51068

5.1 081

51095

51108

51121

51135

51 148

51162

51175

325

51188

51202

51215

51228

51242

51255

51268

51282

51295

51 308

326

51322

51335

51348

51362

51375

51388

51402

51415

51428

51441

327

5145i

51468

51481

51 495.

,51 508.

51521

51534

51548

51561

51574

328

51587

51601

51614

51627*51640

51654

51667

51680

51693

51706

329

51720

51733

51746

51759

51772

51786

51799

51812

51825

51838

330

51851

51865

51878

51891

51904

51917

51930

51943

51957

51970

331

51983

51996

52 009

52 022

52 035

52 048

52 061

52 075

52 088

52 101

332

52114

52 127

52 140

52153

52 166

52 179

52 192

52 205

52 218

52 231

333

52 244

52 257

52 270

52 284

52 297

52 310

52 323

52 336

52 349

52 362

334

52 375

52 388

52 401

52 414

52 427

52 440

52 453

52 466

52 479

52 492

335

52 504

52 517

52 530

52 543

52 556

52 569

52 582

52 595

52 608

52 621

336

52 634

52 647

52 660

52 673

52 686

52 699

52 711

52 724

52 737

52 750

337

52 763

52 776

52 789

52 802

52 815

52 827

52 840

52 853

52 866

52 879

338

52 892

52 905

52 917

52 930

52 943

52 956

52 969

52 982

52 994

53 007

339

53 020

53 033

53 046

53 058

53 071

53 084

53 097

53 110

53 122

53135

340

53 148

53 161

53173

53 186

53 199

53 212

53 224

53 237

53 250

53 263

341

53 275

53 288

53 301

53 314

53 326

53 339

53 352

53 364

53 377

53 390

342

53 403

53 415

53 428

53 441

53 453

53 466

53 479

53 491

53 504

53 517

343

53 529

53 542

53 555

53 567

53 580

53 593

53 605

53 618

53 631

53 643

344

53 656

53 668

53 681

53 694

53 706

53 719

53 732

53 744

53 757

53 769

345

53 782

53 794

53 807

53 820

53 832

53 845

53 857

53 870

53 882

53 895

346

53 908

53 920

53 933

53 945

53 958

53 970

53 983

53 995

54 008

54 020

347

54 033

54 045

54 058

54 070

54 083

54 095

54 108

54 120

54 133

54 145

348

54 158

54 170

54 183

54 195

54 208

54 220

54 233

54 245

54 258

54 270

349

54 283

54 295

54 307

54 320

54 332

54 345

54 357

54 370

54 382

54 394

350

54 407

54 419

54 432

54 444

54 456

54 469

54 481

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54 506

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S

O

1

2

3

4

5

6

7

8

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300-350

350-400

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1

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6

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350

54 407

54 419

54 432

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351

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54 630 54 642

352

54 654

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354

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54 913

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54 937 54 949

54 962

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54 986

54 998 55 011

366

55 023

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55 047

55 060 55 072

55 084

55 096

55 108

55 121 55 133

356

55 14i

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55 206

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357

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358

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359

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55 570

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55 606 55 618

360

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55 642

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55 666 55 678

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55 727 55 739

361

55 751

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55 787 55 799

55 811

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55 847 55 859

362

55 871

55 883

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55 907 55 919

55 931

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55 967 55 979

363

55 991

56 003

56 015

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56 050

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364

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366

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366

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367

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56 561 56 573

368

56 58i

56 597

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56 620 56 632

56 644

56 656

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56 679 56 691

369

56 703

56 714

56 726

56 738 56 750

56 761

56 773

56 785

56 797 56 808

370

56 820

56 832

56 844

56 855 56 867

56 879

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56 902

56 914 56 926

371

56 937

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56 972 56 984

56 996

57 008

57 019

57 031 57 043

372

57 054

57 066

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57 089 57101

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57 1t8 57 159

373

57171

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57 206 57 217

57 229

57 241

57 252

57 264 57 276

374

57 287

57 299

57 310

57 322 57 334

57 345

57 357

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57 380 57 392

376

57 403

57 41i

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57 438 57 449

57461

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57 496 57 507

376

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57 553 57 565

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377

57 634

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378

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379

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57 898 57 910

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380

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382

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383

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384

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386

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386

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393

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394

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306

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396

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406

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71466

71475

71483

71492

71500

71508

519

71517

71525

71533

71542

71550

71559

71567

71575

71584

71592

620

71600

71609

71617

71625

71634

71642

71650

71659

71667

71675

521

71684

71692

71700

71709

71717

71725

71734

71742

71750

71759

522

71767

71775

71784

71792

71800

71809

71817

71825

71834

71842

523

71850

71858

71867

71875

71883

71892

71900

71908

71917

71925

524

71933

71941

71950

71958

71966

71975

71983

71991

71999

72 008

626

72 016

72 024

72 032

72 041

72 049

72 057

72 066

72 074

72 082

72 090

526

72 099

72 107

72 115

72 123

72 132

72140

72 148

72 156

72 165

72 173

527

72 181

72 189

72 198

72 206

72 214

72 222

72 230

72 239

72 247

72 255

528

72 263

72 272

72 280

72 288

72 296

72 304

72 313

72 321

72 329

72 337

529

72 346

72 354

72 362

72 370

72 378

72 387

72 395

72 403

72 411

72 419

630

72 428

72 436

72 444

72 452

72 460

72 469

72 477

72 485

72 493

72 501

531

72 509

72 518

72 526

72 534

72 542

72 550

72 558

72 567

72 575

72 583

532

72 591

72 599

72 607

72 616

72 624

72 632

72 640

72 648

72 656

72 665

533

72 673

72 681

72 689

72 697

72 705

72 713

72 722

72 730

72 738

72 746

534

72 754

72 762

72 770

72 779

72 787

72 795

72 803

72 811

72 819

72 827

636

72 835

72 843

72 852

72 860

72 868

72 876

72 884

72 892

72 900

72 908

536

72 916

72 925

72 933

72 941

72 949

72 957

72 965

72 973

72 981

72 989

537

72 997

73 006

73 014

73 022

73 030

73 038

73 046

73 054

73 062

73 070

538

73 078

73 086

73 094

73 102

73 111

73 119

73 127

73 135

73 143

73 151

539

73159

73 167

73 175

73 183

73 191

73 199

73 207

73 215

73 223

73 231

640

73 239

73 247

73 255

73 263

73 272

73 280

73 288

73 296

73 304

73 312

541

73 320

73 328

73 336

73 344

73 352

73 360

73 368

73 376

73 384

73 392

542

73 400

73 408

73 416

73 424

73 432

73 440

73 448

73 456

73 464

73 472

543

73 480

73 488

73 4%

73 504

73 512

73 520

73 528

73 536

73 544

73 552

544

73 560

73 568

73 576

73 584

73 592

73 600

73 608

73 616

73 624

73 632

546

73 640

73 648

73 656

73 664

73 672

73 679

73 687

73 695

73 703

73 711

546

73 719

73 727

73 735

73 743

73 751

73 759

73 767

73 775

73 783

73 791

547

73 799

73 807

73 815

73 823

73 830

73 838

73 846

73 854

73 862

73 870

548

73 878

73 886

73 894

73 902

73 910

73 918

73 926

73 933

73 941

73 949

549

73 957

73 965

73 973

73 981

73 989

73 997

74 005

74 013

74 020

74 028

560

74 036

74044

74 052

74 060

74 068

74 076

74 084

74 092

74 099

74107

N

1

2

3

4

6

6

7

8

9

600-660

550-600

11

N

O

1

2

3

4

5

74 076

6

7

8

74 099

9

550

74 036

74 044

74 052

74 060

74 068

74 084

74 092

74107

551

74 115

74 123

74131

74 139

74147

74 155

74 162

74 170

74 178

74 186

552

74194

74 202

74 210

74 218

74 225

74 233

74 241

74 249

74 257

74 265

553

74 273

74 280

74 288

74 296

74 304

74 312

74 320

74 327

74 335

74 343

554

74 351

74 359

74 367

74 374

74 382

74 390

74 398

74 406

74 414

74 421

555

74 429

74 437

74 445

74 453

74 461

74 468

74 476

74 484

74 492

74 500

556

74 507

74 515

74 523

74 531

74 539

74 547

74 554

74 562

74 570

74 578

557

74 586

74 593

74 601

74 609

74 617

74 624

74 632

74 640

74 648

74 656

558

74 663

74 671

74 679

74 687

74 695

74 702

74 710

74 718

74 726

74 733

559

74 741

74 749

74 757

74 764

74 772

74 780

74 788

74 796

74 803

74 811

560

74 819

74 827

74 834

74 842

74 850

74 858

74 865

74 873

74 881

74 889

561

74 896

74 904

74 912

74 920

74 927

74 935

74 943

74 950

74 958

74 966

562

74974

74 981

74 989

74 997

75 005

75 012

75 020

75 028

75 035

75 043

563

75 051

75 059

75 066

75 074

75 082

75 089

75 097

75 105

75 113

75 120

564

75 128

75 136

75 143

75 151

75 159

75 166

75 174

75 182

75 189

75 197

565

75 205

75 213

75 220

75 228

75 236

75 243

75 251

75 259

75 266

75 274

566

75 282

75 289

75 297

75 305

75 312

75 320

75 328

75 335

75 343

75 351

567

75 358

75 366

75 374

75 381

75 389

75 397

75 404

75 412

75 420

75 427

568

75 435

75 442

75 450

75 458

75 465

75 473

75 481

75 488

75 496

75 504

569

75 511

75 519

75 526

75 534

75 542

75 549

75 557

75 565

75 572

75 580

570

75 587

75 595

75 603

75 610

75 618

75 626

75 633

75 641

75 648

75 656

571

75 664

75 671

75 679

75 686

75 694

75 702

75 709

75 717

75 724

75 732

572

75 740

75 747

75 755

75 762

75 770

75 778

75 785

75 793

75 800

75 808

573

75 815

75 823

75 831

75 838

75 846

75 853

75 861

75 868

75 876

75 884

574

75 891

75 899

75 906

75 914

75 921

75 929

75 937

75 944

75 952

75 959

575

75 967

75 974

75 982

75 989

75 997

76 005

76 012

76 020

76 027

76 035

576

76 042

76 050

76 057

76 065

76 072

76 080

76 087

76 095

76103

76110

577

76118

76125

76133

76140

76148

76 155

76 163

76 170

76 178

76185

578

76193

76 200

76 208

76 215

76 223

76 230

76 238

76 245

76 253

76 260

579

76 268

76 275

76 283

76 290

76 298

76 305

76 313

76 320

76 328

76 335

580

76 343

76 350

76 358

76 365

76 373

76 380

76 388

76 395

76 403

76 410

581

■ 76 418

76 425

76 433

76 440

76 448

76 455

76 462

76 470»

76 477

76 485

582

76 492

76 500

76 507

76 515

76 522

76 530

76 537

76 545

76 552

76 559

583

76 567

76 574

76 582

76 589

76 597

76 604

76 612

76 619

76 626

76 634

584

76 641

76 649

76 656

76 664

76 671

76 678

76 686

76 693

76 701

76 708

585

76 716

76 723

76 730

76 738

76 745

76 753

76 760

76 768

76 775

76 782

586

76 790

76 797

76 805

76 812

76 819

76 827

76 834

76 842

76 849

76 856

587

76 864

76 871

76 879

76 886

76 893

76 901

76 90S

76 916

76 923

76 930

588

76 938

76 945

76 953

76 960

76967

76 975

76 982

76 989

76 997

77 004

589

77 012

77 019

77 026

77 034

77 041

77 048

77 056

77 063

77 070

77 078

590

77 085

77 093

77100

77107

77115

77122

77129

77137

77 144

77151

591

77159

77166

77173

77181

77188

77195

77 203

77 210

77 217

77 225

592

77 232

77 240

77 247

77 254

77 262

77 269

77 276

7? 283

77 291

77 298

593

77 305

77 313

77 320

77 327

77 335

77 342

77 349

77 357

77 364

77 371

594

77 379

77 386

77 393

77 401

77 408

77 415

77 422

77 430

77 437

77 444

595

77 452

77 459

77 466

77 474

77 481

77 488

77 495

77 503

77 510

77 517

596

77 525

77 532

77 539

77 546

77 554

77 561

77 568

77 576

77 583

77 590

597

77 597

77 605

77 612

77 619

77 627

77 634

77 641

77 648

77 656

77 663

598

77 670

77 677

77 685

77 692

77 699

77 706

77 714

77 721

77 728

77 735

599

77 743

77 750

77 757

77 764

77 772

77 779

77 786

77 793

77 801

77 808

600

77 815

77 822

77 830

77 837

77 844

77 851

77 859
6

77 866

77 873

77 880

N

O

1

2

3

4

5

7

8

9

560-600

12

600-650

K

O

1 2

3

4

5

6

7

8 9

600

77 815

77 822 77 830

77 837

77 844

77 851

77 859

77 866

77 873 77 880

601

77 887

77 895 77 902

77 909

77 916

77 924

77 931

77 938

77 945 77 952

602

77 960

77 967 77 974

77 981

77 988

77 996

78 003

78 010

78 017 78 025

603

78 032

78 039 78 046

78 053

78 061

78 068

78 075

78 082

78 089 78 097

60+

78104

78111 78118

78125

78132

78140

78147

78154

78 161 78 168

606

78176

78183 78190

78197

78 204

78 211

78 219

78 226

78 233 78 240

606

78 247

78 254 78 262

78 269

78 276

78 283

78 290

78 297

78 305 78 312

607

78 319

78 326 78 333

78 340

78 347

78 355

78 362

78 369

78 376 78 383

608

78 390

78 398 78 405

78 412

78 419

78 426

78 433

78 440

78 447 78 455

609

78 462

78 469 78 476

78 483

78490

78 497

78 504

78 512

78 519 78 526

610

78 533

78 540 78 547

78 554

78 561

78 569

78 576

78 583

78 590 78 597

611

78 604

78 611 78 618

78 625

78 633

78 640

78 647

78 654

78 661 78 668

612

78 675

78 682 78 689

78 696

78 704

78 711

78 718

78 725

78 732 78 739

613

78 746

78 753 78 760

78 767

78 774

78 781

78 789

78 796

78 803 78 810

614

78 817

78 824 78 831

78 838

78 845

78 852

78 859

78 866

78 873 78 880

615

78 888

78 895 78 902

78 909

78 916

78 923

78 930

78 937

78 944 78951

616

78 958

78 965 78 972

78 979

78 986

78 993

79 000

79 007

79 014 79 021

617

79 029

79 036 79 043

79 050

79 057

79 064

79 071

79 078

79 085 79 092

618

79 099

79106 79113

79120

79127

79134

79141

79148

79155 79162

619

79169

79176 79183

79190

79197

79 204

79 211

79 218

79 225 79 232

620

79 239

79 246 79 253

79 260

79 267

79 274

79 281

79 288

79 295 79 302

621

79 309

79 316 79 323

79 330

79 337

79 344

79 351

79 358

79 365 79 372

622

79 379

79 386 79 393

79 400

79 407

79 414

79 421

79 428

79 435 79 442

623

79 449

79 456 79 463

79 470

79 477

79 484

79 491

79 498

79 505 79 511

624

79 518

79 525 79 532

79 539

79 546

79 553

79 560

79 567

79 574 79 581

625

79 588

79 59i 79 602

79 609

79 616

79 623

79 630

79 637

79 644 79 650

626

79657

79 664 79 671

79 678

79 685

79 692

79 699

79 706

79 713 79 720

627

79 727

79 734 79 741

79 748

79 754

79 761

79 768

79 775

79 782 79 789

628

79 796

79 803 79 810

79 817

79 824

79 831

79 837

79 844

79 851 79 858

629

79 865

79872 79 879

79 886

79 893

79 900

79 906

79 913

79 920 79 927

630

79934

79941 79948

79955

79 962

79 969

79 975

79 982

79 989 79996

631

80 003

80 010 80 017

80024

80 030

80037

80 044

80 051

80 058 80065

632

80072

80 079 80 085

80 092

80 099

80106

80113

80120

80127 80134

633

80140

80147 80154

80161

80168

80175

80182

80188

80195 80 202

634

80 209

80 216 80 223

80 229

80 236

80 243

80 250

80 257

80 264 80 271

635

80 277

80 284 80 291

80 298

80 305

80 312

80 318

80 325

80 332 80 339

636

80 346

80353 80 359

80 366

80 373

80 380

80 387

80393

80 400 80 407

637

80 414

80421 80428

80434

80 441

80 448

80 455

80 462

80 468 80 475

638

80 482

80 489 80496

80 502

80 509

80 516

80 523

80 530

80 536 80 543

639

80550

80 557 80 564

80 570

80 577

80 584

80 591

80 598

80 604 80 611

640

80 618

80 625 80 632

80638

80 645

80652

80 659

80 665

80 672 80 679

641

80 686

80 693 80 699

80 706

80 713

80 720

80 726

80 733

80 740 80 747

642

80 754

80 760 80 767

80 774

80 781

80 787

80 79^

80 801

80 808 80 814

643

80 821

80 828 80 835

80 841

80 848

80 855

80 862

80 868

80 875 80 882

644

80889

80 895 80 902

80 909

80 916

80922

80 929

80 936

80 943 80 949

645

80956

80 963 80969

80976

80983

80 990

80 996

81003

81010 81017

646

81023

81030 81037

81043

81050

81 057

81064

81070

81077 81084

647

81090

81097 81104

81111

81117

81124

81131

81137

81 144 81 151

648

81158

81164 81171

81178

81184

81191

81198

81204

81211 81218

649

81224

81231 81238

81245

81251

81258

81265

81271

81278 81285

650

81291

81298 81305

81311

81318

81325

81331

81338

81345 81351

N

1 2

8

4

5

6

7

8 9

600-650

650-700

18

N

81291

1

2

3

4

5

6

7

81338

8

9

650

81298

81305

81311

81318

8132i

81331

81345

81351

651

81358

81365

81371

81378

81385

81391

81398

81405

81411

81418

652

81425

81431

81438

81445

81451

81458

8146i

81471

81478

81485

653

81491

81498

81505

81511

81518

8152i

81531

81538

81544

81551

654

81558

81564

81571

81578

81584

81591

81598

81604

81611

81617

655

81624

81631

81637

81644

81 651

81657

81664

81671

81677

81684

656

81690

81697

81704

81710

81717

81723

81730

81737

81743

81750

657

81757

81 763

81770

81776

81783

81790

81796

81803

81809

81816

658

81823

81829

81836

81842

81849

81856

81862

81869

81875

81882

659

81889

8189i

81902

81908

81915

81921

81928

81935

81941

81948

660

81954

81961

81968

81974

81981

81987

81994

82 000

82 007

82 014

661

82 020

82 027

82 033

82 040

82 046

82 053

82 060

82 066

82 073

82 079

662

82 086

82 092

82 099

82 105

82 112

82119

82 125

82 132

82 138

82 145

663

82 151

82 158

82 164

82 171

82 178

82 184

82 191

82 197

82 204

82 210

664

82 217

82 223

82 230

82 236

82 243

82 249

82 256

82 263

82 269

82 276

665

82 282

82 289

82 295

82 302

82 308

82 315

82 321

82 328

82 334

82 341

666

82 347

82 354

82 360

82 367

82 373

82 380

82 387

82 393

82 400

82 406

667

82 413

82 419

82 426

82 432

82 439

82 445

82 452

82 458

82 465

82 471

668

82 478

82 484

82 491

82 497

82 504

82 510

82 517

82 523

82 530

82 536

669

82 543

82 549

82 556

82 562

82 569

82 575

82 582

82 588

82 595

82 601

670

82 607

82 614

82 620

82 627

82 633

82 640

82 646

82 653

82 659

82 666

671

82 672

82 679

82 685

82 692

82 698

82 705

82 711

82 718

82 724

82 730

672

82 737

82 743

82 750

82 756

82 763

82 769

82 776

82 782

82 789

82 795

673

82 802

82 808

82 814

82 821

82 827

82 834

82 840

82 847

82 853

82 860

674

82 866

82 872

82 879

82 885

82 892

82 898

82 905

82 911

82 918

82 924

675

82 930

82 937

82 943

82 950

82 956

82 963

82 969

82 975

82 982

82 988

676

82 995

83 001

83 008

83 014

83 020

83 027

83 033

83 040

83 046

83 052

677

83 059

83 065

83 072

83 078

83 085

83 091

83 097

83 104

83 110

83 117

678

83 123

83 129

83 136

83 142

83 149

83 155

83 161

83 168

83 174

83 181

679

83 187

83 193

83 200

83 206

83 213

83 219

83 225

83 232

83 238

83 245

680

83 251

83 257

83 264

83 270

83 276

83 283

83 289

83 296

83 302

83 308

681

83 315

83 321

83 327

83 334

83 340

83 347

83 353

83 359

83 366

83 372

682

83 378

83 385

83 391

83 398

83 404

83 410

83 417

83 423

83 429

83 436

683

83 442

83 448

83 455

83 461

83 467

83 474

83 480

83 487

83 493

83 499

684

83 506

83 512

83 518

83 525

83 531

83 537

83 544

83 550

83 556

83 563

685

83 569

83 575

83 582

83 588

83 594

83 601

83 607

83 613

83 620

83 626

686

83 632

83 639

83 645

83 651

83 658

83 664

83 670

83 677

83 683

83 689

687

83 6%

83 702

83 708

83 715

83 721

83 727

83 734

83 740

83 746

83 753

688

83 759

83 765

83 771

83 778

83 784

83 790

83 797

83 803

83 809

83 816

689

83 822

83 828

83 835

83 841

83 847

83 853

83 860

83 866

83 872

83 879

690

83 885

83 891

83 897

83 904

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83 916

83 923

83 929

83 935

83 942

691

83 948

83 954

83 960

83 967

83 973

83 979

83 985

83 992

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84 004

692

84 011

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84 036

84 042

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84 073

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84 105

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84 292

84 298

84 305

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700

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84 547

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84 559

84 566

K

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5

6

7

8

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660-700

14

700-750

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1 2

3

4

5

6

7

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700

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84 516 84 522

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84 652

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84 702 84 708

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84 763 84 770

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84 819

84 825 84 831

84 837

84 844

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84 880

84 887 84 893

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84 960

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85 003

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710

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85 327

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86 249

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1 2

3

4

5

6

7

8

700-760

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4

5

6

7

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750

87 506

87 512

87 518

87 523

87 529

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88 001

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88 649

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88 672

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88 694

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88 705

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88 762

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88 846

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89 003

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1

2

3

4

5

6

7

8

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800-850

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O

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6

6

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93 059

93 064

93 069

93 075

93 080

93 085

93 090

853

93 095

93 100

93 105

93 110

93 115

93 120

93 125

93 131

93 136

93 141

854

93 146

93 151

93 156

93 161

93 166

93 171

93 176

93 181

93 186

93 192

855

93 197

93 202

93 207

93 212

93 217

93 222

93 227

93 232

93 237

93 242

856

93 247

93 252

93 258

93 263

93 268

93 273

93 278

93 283

93 288

93 293

857

93 298

93 303

93 308

93 313

93 318

93 323

93 328

93 334

93 339

93 344

858

93 349

93 354

93 359

93 364

93 369

93 374

93 379

93 384

93 389

93 394

859

93 399

93 404

93 409

93 414

93 420

93 425

93 430

93 435

93 440

93 445

860

93 450

93 45'5

93 460

93 465

93 470

93 475

93 480

93 485

93 490

93 495

861

93 500

93 505

93 510

93 515

93 520

93 526

93 531

93 536

93 541

93 546

862

93 551

93 556

93 561

93 566

93 571

93 576

93 581

93 586

93 591

93 596

863

93 601

93 606

93 611

93 616

93 621

93 626

93 631

93 636

93 641

93 646

864

93 651

93 656

93 661

93 666

93 671

93 676

93 682

93 687

93 692

93 697

865

93 702

93 707

93 712

93 717

93 722

93 727

93 732

93 737

93 742

93 747

866

93 752

93 757

93 762

93 767

93 772

93 777

93 782

93 787

93 792

93 797

867

93 802

93 807

93 812

93 817

93 822

93 827

93 832

93 837

93 842

93 847

868

93 852

93 857

93 862

93 867

93 872

93 877

93 882

93 887

93 892

93 897

869

93 902

93 907

93 912

93 917

93 922

93 927

93 932

93 937

93 942

93 947

870

93 952

93 957

93 962

93 967

93 972

93 977

93 982

93 987

93 992

93 997

871

94 002

94 007

94 012

94 017

94 022

94 027

94 032

94 037

94 042

94 047

872

94 052

94 057

94 062

94 067

94 072

94 077

94 082

94 086

94 091

94 096

873

94 101

94 106

94 111

94 116

94 121

94 126

94 131

94 136

94 141

94 146

874

94151

94 156

94 161

94 166

94171

94 176

94 1§1

94 186

94 191

94 196

875

94 201

94 206

94 211

94 216

94 221

94 226

94 231

94 236

94 240

94 245

876

94 250

94 255

94 260

94 265

94 270

94 275

94 280

94 285

94 290

94 295

877

94 300

94 305

94 310

94 315

94 320

94 325

94 330

94 335

94 340

94 345

878

94 349

94 354

94 359

94 364

94 369

94 374

94 379

94 384

94 389

94 394

879

94 399

94 404

94 409

94 414

94 419

94 424

94 429

94 433

94 438

94 443

880

94 448

94 453

94 458

94 463

94 468

94 473

94 478

94 483

94 488

94 493

881

94 498

94 503

94 507

94 512

94 517

94 522

94 527

94 532

94 537

94 542

882

94 547

94 552

94 557

94 562

94 567

94 571

94 576

94 581

94 586

94 591

883

94 596

94 601

94 606

94 611

94 616

94 621

94 626

94 630

94 635

94 640

884

94 645

94 650

94 655

94 660

94 665

94 670

94 675

94 680

94 685

94 689

885

94 694

94 699

94 704

94 709

94 714

94 719

94 724

94 729

94 734

94 738

886

94 743

94 748

94 753

94 758

94 763

94 768

94 773

94 778

94 783

94 7S7

887

94 792

94 797

94 802

94 807

94 812

94 817

94 822

94 827

94 832

94 836

888

94 841

94 846

94 851

94 856

94 861

94 866

94 871

94 876

94 880

94 885

889

94 890

94 895

94 900

94 905

94 910

94 915

94 919

94 924

94 929

94 934

890

94 939

94 944

94 949

94 954

94 959

94 963

94 968

94 973

94 978

94 983

891

94 988

94 993

94 998

95 002

95 007

95 012

95 017

95 022

95 027

95 032

892

95 036

95 041

95 046

95 051

95 056

95 061

95 066

95 071

95 075

95 080

893

95 085

95 090

95 09i

95 100

95 105

95 109

95 114

95 119

95 124

95 129

894

95 134

95 139

95 143

95 148

95 153

95 158

95 163

95 168

95 173

95 177

895

95 182

95 187

95 192

95 197

95 202

95 207

95 211

95 216

95 221

95 226

896

95 231

95 236

95 240

95 245

95 250

95 255

95 260

95 265

95 270

95 274

897

95 279

95 284

95 289

95 294

95 299

95 303

95 308

95 313

95 318

95 323

898

95 328

95 332

95 337

95 342

95 347

95 352

95 357

95 361

95 366

95 371

899

95 376

95 381

95 386

95 390

95 395

95 400

95 405

95 410

95 415

95 419

900

95 424

95 429

95 434

95 439
3

95 444

95 448

95 453

95 458
7

95 463

95 468
9

N

1

2

4

6

6

8

850-900

18

900-950

N

1 2

3

4

5

6

7

8

9

900

95 424

95 429 95 434

95 439

95 444

95 448

95 453

95 458

95 463

95 468

901

95 472

95 477 95 482

95 487

95 492

95 497

95 501

95 506

95 511

95 516

902

95 521

95 525 95 530

95 535

95 540

95 545

95 550

95 554

95 559

95 564

903

95 569

95 574 95 578

95 583

95 588

95 593

95 598

95 602

95 607

95 612

90+

95 617

95 622 95 626

95 631

95 636

95 641

95 646

95 650

95 655

95 660

905

95 665

95 670 95 674

95 679

95 684

95 689

95 694

95 698

95 703

95 708

906

95 713

95 718 95 722

95 727

95 732

95 737

95 742

95 746

95 751

95 756

907

95 761

95 766 95 770

95 775

95 780

95 785

95 789

95 794

95 799

95 804

908

95 809

95 813 95 818

95 823

95 828

95 832

95 837

95 842

95 847

95 852

909

95 856

95 861 95 866

95 871

95 875

95 880

95 885

95 890

95 895

95 899

910

95 904

95 909 95 914

95 918

95 923

95 928

95 933

95 938

95 942

95 947

911

95 952

95 957 95 961

95 966

95 971

95 976

95 980

95 985

95 990

95 995

912

95 999

96004 96009

96 014

96 019

96 023

96 028

96 033

96 038

96 042

913

96 047

96 052 96 057

96 061

96 066

96 071

96 076

96 080

96 085

96 090

914

96 095

96 099 961(H

96109

96 114

96118

96123

96128

96133

96 137

915

96142

96147 96152

96156

96161

96166

96171

96175

96180

96185

916

96190

96194 96199

96 204

96 209

96 213

96 218

96 223

96 227

96232

917

96 237

96 242 96 246

96 251

96 256

96 261

96 265

96 270

96 275

96 280

918

96 284

96 289 96 294

96 298

96 303

96 308

96 313

96 317

96 322

96 327

919

96 332

96 336 96 341

96 346

96 350

96 355

96 360

96 365

96 369

96 374

920

96 379

96 384 96 388

96 393

96 398

96 402

96 407

96 412

96 417

96 421

921

96 426

96 431 96 435

96 440

96 445

96 450

96 454

96 459

96 464

96 468

922

96 473

96 478 96 483

96 487

96 492

96 497

96 501

96 506

96 511

96 515

923

96 520

96 525 96 530

96 534

96 539

96 544

96 548

96 553

96 558

96 562

924

%567

96 572 96 577

96 581

96 586

96 591

96 595

96 600

96 605

96 609

925

96 614

96 619-96 624

96 628

96 633

96 638

96 642

96 647

96 652

96 656

926

96 661

96 666 96 670

96 675

96 680

96 685

96 689

96 694

96 699

96 703

927

96 708

96 713 96 717

96 722

96 727

96 731

96 736

96 741

96 745

96 750

928

96 755

96 759 96 764

96 769

96 774

96 778

96 783

96 788

96 792

96 797

929

96 802

96 806 96 811

96 816

96 820

96 825

96 830

96 834

96 839

96 844

930

96 848

96 853 96 858

96 862

96 867

96 872

96 876

96 881

96 886

96 890

931

96 895

96 900 96 904

96 909

96 914

96 918

96 923

96 928

96 932

96 937

932

96 942

96 946 96 951

96 956

96 960

96 965

96 970

96 974

96 979

96 984

933

96 988

96 993 96 997

97 002

97 007

97 011

97 016

97 021

97 025

97 030

934

97 035

97 039 97 044

97 049

97 053

97 058

97 063

97 067

97 072

97 077

935

97 081

97 086 97 090

97 095

97100

97 104

97109

97114

97118

97 123

936

97128

97132 97 137

97 142

97146

97151

97155

97160

97 165

97 169

937

97174

97179 97 183

97 188

97 192

97197

97 202

97 206

97 211

97 216

938

97 220

97 225 97 230

97 234

97 239

97 243

97 248

97 253

97 257

97 262

939

97 267

97 271 97 276

97 280

97 285

97 290

97 294

97 299

97 304

97 308

940

97 313

97 317 97 322

97 327

97 331

97 336

97 340

97 345

97 350

97 354

941

97 359

97 364 97 368

97 373

97 377

97 382

97 387

97 391

97 396

97 400

942

97 405

97 410 97 414

97 419

97 424

97 428

97 433

97 437

97 442

97 447

943

97 451

97 456 97 460

97 465

97 470

97 474

97 479

97 483

97 488

97 493

944

97 497

97 502 97 506

97 511

97 516

97 520

97 525

97 529

97 534

97 539

945

97 543

97 548 97 552

97 557

97 562

97 566

97 571

97 575

97 580

97 585

946

97 589

97 594 97 598

97 603

97 607

97 612

97 617

97 621

97 626

97 630

947

97 635

97 640 97 644

97 649

97 653

97 658

97 663

97 667

97 672

97 676

948

97 681

97 685 97 690

97 695

97 699

97 704

97 708

97 713

97 717

97 722

949

97 727

97 731 97 736

97 740

97 745

97 749

97 754

97 759

97 763

97 768

950

97 772

97 777 97 782

97 786

97 791

97 795

97 800

97 804

97 809

97 813

N

O

1 2

3

4

5

6

7

8

9

900 IT 950

950-1000

19

N

o

1

2

3

4

5

6

7

8

9

950

97 772

97 777

97 782

97 786

97 791

97 795

97 800

97 804

97 809

97 813

951

97 818

97 823

97 827

97 832

97 836

97 841

97 845

97 850

97 85i

97 859

952

97 864

97 868

97 873

97 877

97 882

97 886

97 891

97 896

97 900

97 90i

953

97 909

97 914

97 918

97 923

97 928

97 932

97 937

97 941

97 946

97 950

954

97 95i

97 959

97 964

97 968

97 973

97 978

97 982

97 987

97 991

97 996

965

98 000

98 005

98 009

98 014

98 019

98 023

98 028

98 032

98 037

98 041

956

98 046

98 050

98 05i

98 059

98 064

98 068

98 073

98 078

9S082

98 087

957

98 091

98 096

98100

98105

98 109

98114

98118

98123

98127

98 132

958

98137

98 141

98146

98150

98155

98159

98164

98168

98173

98 177

959

98182

98186

98191

98195

98 200

98 204

98 209

98 214

98 218

98 223

960

98 227

98 232

98 236

98 241

98 245

98 250

98 254

98 259

98 263

98 268

961

98 272

98 277

98 281

98 286

98 290

98 295

98 299

98 304

98 308

98 313

962

98 318

98 322

98 327

98 331

98 336

98 340

98 345

98 349

98 354

98 358

963

98 363

98 367

98 372

98 376

98 381

98 385

98 390

98 394

98 399

98 403

964

98 408

98 412

98 417

98 421

98 426

98 430

98 43i

98 439

98 444

98 448

965

98 453

98 457

98 462

98 466

98 471

98 475

98 480

98 484

98 489

98 493

966

98 498

98 502

98 507

98 511

98 516

98 520

98 525

98 529

93 534

98 538

967

98 543

98 547

98 552

98 556

98 561

98 565

98 570

98 574

98 579

98 583

968

98 588

98 592

98 597

98 601

98 605

98 610

98 614

98 619

98 623

98 628

969

98 632

98 637

98 641

98 646

98 650

98 655

98 659

98 664

98 668

98 673

970

98 677

98 682

98 686

98 691

98 695

98 700

98 704

98 709

98 713

98 717

971

98 722

98 726

98 731

98 735

98 740

98 744

98 749

98 753

98 758

98 762

972

98 767

98 771

98 776

98 780

98 784

98 789

98 793

98 798

98 802

98 807

973

98 811

98 816

98 820

98 825

98 829

98 834

98 838

98 843

98 847

98 851

974

98 856

98 860

98 865

98 869

98 874

98 878

98 883

98 887

98 892

98 896

975

98 900

98 905

98 909

98 914

98 918

98 923

98 927

98 932

98 936

98 941

976

98 945

98 949

98 954

98 958

98 963

98 967

98 972

98 976

98 981

98 985

977

98 989

98 994

98 998

99 003

99 007

99 012

99 016

99 021

99 025

99 029

978

99 034

99 038

99 043

99 047

99 052

99 056

99 061

99 065

99 069

99 074

979

99 078

99 083

99 087

99 092

99 096

99 100

99105

99109

99114

99118

980

99123

99127

99131

99 136

99140

99145

99149

99154

99158

99162

981

99167

99171

99176

99 180

99 185

99189

99193

99198

99 202

99 207

982

99 211

99 216

99 220

99 224

99 229

99 233

99 238

99 242

99 247

99 251

983

99 255

99 260

99 264

99 269

99 273

99 277

99 282

99 286

99 291

99 295

984

99 300

99 304

99 308

99 313

99 317

99 322

99 326

99 330

99 335

99 339

985

99 344

99 348

99 352

99 357

99 361

99 366

99 370

99 374

99 379

99 383

986

99 388

99 392

99 396

99 401

99 405

99 410

99 414

99 419

99 423

99 427

987

99 432

99 436

99 441

99 445

99 449

99 454

99 458

99 463

99 467

99 471

988

99 476

99 480

99 484

99 489

99 493

99 498

99 502

99 506

99 511

99 515

989

99 520

99 524

99 528

99 533

99 537

99 542

99 546

99 550

99 555

99 559

990

99 564

99 568

99 572

99 577

99 581

99 585

99 590

99 594

99 599

99 603

991

99 607

99 612

99 616

99 621

99 625

99 629

99 634

99 638

99 642

99 647

992

99 651

99 656

99 660

99 664

99 669

99 673

99 677

99 682

99 686

99 691

993

99 695

99 699

99 704

99 708

99 712

99 717

99 721

99 726

99 730

99 734

994

99 739

99 743

99 747

99 752

99 756

99 760

99 765

99 769

99 774

99 778

995

99 782

99 787

99 791

99 795

99 800

99 804

99 808

99 813

99 817

99 822

996

99 826

99 830

99 835

99 839

99 843

99 848

99 852

99 856

99 861

99 865

997

99 870

99 874

99 878

99 883

99 887

99 891

99 896

99 900

99 904

99 909

998

99 913

99 917

99 922

99 926

99 930

99 935

99 939

99 944

99 948

99 952

999

99 957

99 961

99 965

99 970

99 974

99 978

99 983

99 987

99 991

99 996

1000

00 000

00 004

00 009
2

00 013
3

00 017

00 022

00 026

00 030

00 03i

00 039

N

1

4

5

6

7

8

9

950-1000

20 TABLE IT.-LOGAETTHMS OF CONSTANTS.

Circumference of the Circle in degrees = 360

Circumference of the Circle in minutes = 21 600

Circumference of the Circle in seconds =1 296 000

If the radius ?• = 1, half the Circumference of the Circle is
JT = 3. 14 159 265 358 979 323 846 264 338 328

log
2. 55 630 250
4. 33 445 375
6.11260 500

0. 49 714 987

Also :
2,r= 6.28 318 531

4 7r= 12.56 637 061

'!^= 1.57 079 633

1. 04 719 755

= 4.18 879 020

= 0.78 539816

-= 0.52 359 878
6

-= 0.31830 989

2^
3

= 0.15 915 494

-= 0.95 492 966

TT

-= 1.27 323 954

— = 0.23 873 241
47r

log
0.79 817 987
1.09 920 986
0.19 611988

0. 02 002 862

0. 62 208 861

9. 89 508 988 - 10

9.71899862- 10

9. 50 285 013 - 10

9. 20 182 013 - 10

9. 97 997 138 - 10

0.10 491012

9. 37 791 139 - 10

1

4-

1

3( 3

V4T

= 9. 86 %0 440
-0.10132 118
= 1. 77 245 385
= 0. 56 418 958

0. 97 720 502

1.12 837 917

1.46 459189
0. 68 278 406

2. 14 502 940
0. 62 035 049

S/tt
A/6

- = 0. 80 599 598

log
0. 99 429 975

9. 00 570 025 - 10

0.24 857 494

9. 75 142 506 - 10

9. 98 998 569 - 10

0. 05 245 506
0. 16 571 662
9. 83 428 338 - 10

0. 33 143 325

9. 79 263 713 - 10

9. 90 633 287 - 10

Arc a, whose length is equal to the radius r, is

180

in degrees a° = — . . .

TT

in minutes a' ^10800.

= 57.29 577 951°.
= 3 437. 74 677' . .

in seconds a" _ 648 000 = 206 264. 806" ,

TT

Arc 2 a, whose length is equal to twice the radius, 2 r, is :

360

in degrees 2 a° = — . . .

TT

. . o / 21 600
m mmutes 2 a' =

= 114. 59 155 903°
= 6 875.49 354'..

in seconds 2 a" .... = ^ ^^ ^^^ . . . = 412 529. 612" . .

If the radius r = 1, the length of the arc is :

1 TT

for 1 degree .
for 1 minute ,
for 1 second .
for J degree .
for i minute,
for i second .

a'"'
J_

a"' ■ ■
1

2a°'

1
2 a'"

1
2 a"'

180

10 800

ir

648 000"

TT

360"'"'

21600

. . = 0. 01 745 329. . .
..= 0.00 029 089.
.. = 0.00 000 48i...
. . = 0. 00 872 66i. . .
. . = 0. 00 014 544. . .
. . = 0. 00 000 242. . .

1 296 000
Sin !'• in the unit circle = 0. 00 000 48i

log

1. 75 812 263

3. 53 627 388
5.31442 513

2. 05 915 263

3. 83 730 388
S. 61 545 513

8. 24 187 737 - 10
6.46372 612- 10
4. 68 557 487 - 10
7. ?4 084 737-10
6. 16 269 612 - 10
4. 38 454 487 - 10
4.68 557 487- 10

21

TABLE TTT.

w

THE LOGAEITHMS

OF THB

TRIGONOMETRIC

FUNCTIONS :

Prom O'' to 0° 3', or 89° 57' to 90°, for every second ;

From 0° to 2°, or 88°

to 90°, for

every ten seconds ;

Prom 1° t(
Note. T

log sin

) 89°, for every minute

is to be a

log
log

ppended.

tan = log sin
003 = 10,00 000

all the logarithms — ]

0°

ff

o

0'

1'

2'

tf

tf

O'

1'

2'

tf
30

„

6. 46 373

6.76 476

60

30

6. 16 270

6. 63 982

6. 86 167

1

4. 68 557

6. 47 090

6. 76 836

59

31

6. 17 694

6. 64 462

6. 86 455

29

2

4. 98 660

6. 47 797

6. 77 193

58

32

6. 19 072

6. 64 936

6. 86 742

28

3

5. 16 270

6. 48 492

6. 77 548

57

33

6. 20 409

6. 65 406

6. 87 027

27

4

5. 28 763

6. 49 175

6. 77 900

56

34

6. 21 70S

6. 65 870

6.87 310

26

5

5. 38 454

6. 49 849

6. 78 248

65

35

6. 22 964

6. 66 330

6. 87 591

25

6

5.46 373

6.50 512

6. 78 595

54

36

6. 24 188

6. 66 785

6. 87 870

24

7

5. 53 067

6. 51 165

6. 78 938

53

37

6. 25 378

6. 67 235

6. 88 147

23

8

5. 58 866

6. 51 808

6. 79 278

52

38

6. 26 536

6. 67 680

6. 88 423

22

9

5. 63 982

6. 52 442

6. 79 616

51

39

6. 27 664

6. 68 121

6. 88 697

21

10

5. 68 557

6. 53 067

6. 79 952

50

40

6. 28 763

6. 68 557

6. 88 969

20

11

5.72 697

6. 53 683

6. 80 285

49

41

6. 29 836

6. 68 990

6. 89 240

19

12

5. 76 476

6. 54 291

6. 80 61i

48

42

6. 30 882

6. 69 418

6. 89 509

18

13

5.79 952

6. 54 890

6. 80 943

47

43

6.31904

6. 69 841

6. 89 776

17

14

5. 83 170

6. 55 481

6. 81 268

46

44

6. 32 903

6. 70 261

6. 90 042

16

15

5. 86 167

6. 56 064

6. 81 591

45

45

6. 33 879

6. 70 676

6. 90 306

15

16

5. 88 969

6. 56 639

6. 81 911

44

46

6. 34 833

6. 71 088

6. 90 568

14

17

5. 91 602

6. 57 207

6. 82 230

43

47

6. 35 767

6. 71 496

6. 90 829

13

18

5. 94 085

6. 57 767

6. 82 545

42

48

6. 36 682

6.71900

6. 91 088

12

19

5.96433

6. 58 320

6. 82 859

41

49

6.37 577

6. 72 300

6. 91 346

11

20

5.98 660

6. 58 866

6. 83 170

40

50

6. 38 454

6. 72 697

6. 91 602

10

21

6. 00 779

6. 59 406

6. 83 479

39

51

6.39 315

6.73 090

6. 91 857

9

22

6. 02 800

6. 59 939

6. 83 786

38

52

6. 40 158

6. 73 479

6.92 110

8

23

6. 04 730

6. 60 465

6. 84 091

37

53

6.40 985

6. 73 865

6. 92 362

7

24

•6. 06 579

6. 60 985

6. 84 394

36

54

6. 41 797

6. 74 248

6. 92 612

6

25

6. 08 351

6. 61 499

6. 84 694

35

55

6. 42 594

6. 74 627

6. 92 861

5

26

6. 10 055

6. 62 007

6. 84 993

34

56

6. 43 376

6. 75 003

6. 93 109

4

27

6. 11 694

6. 62 509

6. 85 289

33

57

6. 44 145

6. 75 376

6. 93 355

3

28

6. 13 273

6. 63 006

6. 85 584

32

58

6.44 900

6. 75 746

6. 93 599

2

29

6. 14 797

6. 63 496

6. 85 876

31

59

6. 45 643

6. 76 112

6. 93 843

1

30

6. 16 270

6. 63 982

6. 86 167

30

60

6. 46 373

6.76 476

6. 94 085

ft

59'

58'

57'

tf

tf

59'

58'

57'

tt

log cot = log 00 s
log sin = 10. 00 000

89^

log cos

22

0°

f "

log sin

log tan

log cos

tt 1

' f log sin

log tan

log cos

"1

O

10.00000

6O

10 7.46 373

7. 46 373

10.00000 10 sol

10

5.68 557

5: 68 557

10.00000

50

10

7.47 090

7. 47 091

10.00000

50

20

5.98 660

5.98 660

1000000

40

20

7. 47 797

7. 47 797

10.00000

40

30

6. 16 270

6. 16 270

10.00000 1 30

30

7.48 491

7. 48 492

1000000

30

40

6. 28 763

6. 28 763

10.00000 20

40

7. 49 175

7. 49 176

10.00000

20

50

6. 38 454

6. 38 454

10.00000 10

50

7. 49 849

7. 49 849

10.00000

10

1

6.46 373

6. 46 373

10.00000 59

110

7.50 512

7.50 512

10.00000

49

10

6. 53 067

6. 53 067

10.00000 50

10

7. 51 165

7. 51 165

10.00000

50

20

6. 58 866

6. 58 866

10.00000

40

20

7. 51 808

7. 51 809

10.00000

40

30

6. 63 982

6. 63 982

10.00000

30

30

7. 52 442

7. 52 443

10.00000

30

40

6.68 557

6.68 557

10.00000

20

40

7. 53 067

7. 53 067

10.00000 1 20

50

6. 72 697

6. 72 697

10.00000

10

50

7. 53 683

7. 53 683

10.00000 j 10

2

6.76 476

6.76 476

10 00000^

58

12

7. 54 291

7. 54 291

10 00000 [0 48

10

6.79 952

6. 79 952

10.00000

50

10

7. 54 890

7. 54 890

10.00000 ! 50

20

6. 83 170

6. 83 170

10.00000

40

20

7. 55 481

7. 55 481

1000000! 40

30

6. 86 167

6. 86 167

10.00000

30

30

7.56 064

7. 56 064

10.00000 ! 30

40

6. 88 969

6. 88 969

10.00000

20

40

7. 56 639

7. 56 639

10.00000

20

50

6. 91 602

6. 91 602

10.00000

10

50

7. 57 206

7. 57 207

10.00000

10

3

6. 94 085

6.94 085

1000000

057

13

7. 57 767

7. 57 767

10.00000

47

10

6.96 433

6.96 433

10.00000

50

10

7. 58 320

7. 58 320

10.00000

50

20

6.98 660

6. 98 661

10.00000

40

20

7. 58 866

7. 58 867

1000000

40

30

7. 00 779

7. 00 779

10.00000

30

30

7.59 406

7.59 406

10.00000

30

40

7. 02 800

7. 02 800

10.00000

20

40

7.59 939

7. 59 939

10.00000

20

50

7. 0+ 730

7. 04 730

10.00000

10

50

7.60 465

7.60466

10.00000

10

4

7. 06 579

7. 06 579 ■

10.00000 ! 56 1

14

7. 60 985

7. 60 986

10.00000 46

10

7.08 351

7. 08 352

10.00000

50

10

7. 61 499

7. 61 500

10.00000 50

20

7.10055

7.10055

10.00000

40

20

7. 62 007

7. 62 008

10.00000 ! 40

30

7.11694

7.11694

10.00000

30

30

7. 62 509

7.62 510

10.00000 i 30

40

7. 13 273

7. 13 273

10.00000

20

40

7.63 006

7. 63 006

10.00000 20

50

7. 14 797

7. 14 797

10.00000

10

50

7. 63 496

7. 63 497

10.00000 1 10

5

7. 16 270

7. 16 270

10.00000

55

15

7. 63 982

7. 63 982

10.00000 i 45

10

7. 17 694

7. 17 694

10.00000

50

10

7. 64 461

7. 64 462

10.00000 : 50

20

7.19 072

7. 19 073

10.00000

40

20

7. 64 936

7.64 937

10.00000 40

30

7.20409

7.20 409

10.00000

30

30

7. 65 406

7. 65 406

10.00000 30

40

7. 21 705

7. 21 705

10 00000

20

40

7. 65 870

7. 65 871

10.00000 20

50

7. 22 964

7. 22 964

10.00000

10

50

7. 66 330

7.66 330

10.00000 1 10

6

7. 24 188

7. 24 188

10.00000

54

16

7. 66 784

7. 66 785

10.00000 1 44

10

7. 25 378

7. 25 378

10.00000

50

10

7. 67 235

7. 67 235

10.00000 1 50

20

7. 26 536

7.26536

10.00000

40

20

7. 67 680

7. 67 680

10.00000 40

30

7.27 664

7. 27 664

10.00000

30

30

7. 68 121

7. 68 121

10.00000 i 30

40

7. 28 763

7. 28 764

10.00000

20

40

7.68 557

7. 68 558

9.99999 20

50

7. 29 836

7. 29 836

10.00000

10

50

7. 68 989

7.68 990

9.99999

10

7

7. 30 882

7. 30 882

1000000

53

170

7. 69 417

7.69 418

9.99 999

43

10

7.31904

7.31904

10.00000

50

10

7. 69 841

7. 69 842

9.99 999

50

20

7. 32 903

7. 32 903

10.00000

40

20

7. 70 261

7. 70 261

9.99 999

40

30

7. Z2, 879

7. 33 879

1000000

30

30

7.70 676

7.70 677

9.99 999

30

40

7. 34 833

7. 34 833

10.00000

20

40

7. 71 088

7. 71 088

9.99 999

20

50

7. 35 767

7. 35 767

10.00000

10

50

7. 71 496

7. 71 496

9.99 999

10

8

7.36 682

7.36 682

10.00000

52

18

7.71900

7.71900

9.99 999

42

10

7.37 577

7.37 577

10.00000

50

10

7. 72 300

7. 72 301

9.99 999

50

20

7. 38 454

7. 38 455

10.00000

40

20

7. 72 697

7. 72 697

9.99 999

40

30

7.39 314

7.39 315

10.00000

30

30

7.73 090

7. 73 090

9.99 999

30

40

7. 40 158

7.40158

10.00000

20

40

7. 73 479

7. 73 480

9.99 999

20

50

7.40 985

7.40 985

10.00000

10

50

7. 73 865

7. 73 866

9.99 999

10

9

7. 41 797

7. 41 797

10.00000

051

190

7. 74 248

7. 74 248

9.99 999

41

10

7. 42 594

7. 42 594

10.00000

50

10

7. 74 627

7. 74 628

9.99 999

50

20

7. 43 376

7. 43 376

1000000

40

20

7. 75 003

7.75 004

9.99 999

40

30

7. 44 145

7. 44 145

10.00000

30

30

7. 75 376

7. 75 377

9.99 999

30

40

7.44 900

7.44 900

10.00000

20

40

7. 75 745

7. 75 746

9.99 999

20

50

7. 45 643

7. 45 643

10.00000

10

50

7. 76 112

7. 76 113

9.99 999

10

lOO

7.46373

7. 46 373

10.00000

5O

20

7.76 475

7.76476

9.99 999

04O

t tt

log cos

log cot

log sin

tt t

1 tt

log cos

log cot

log sin

tt t

m

0^

28

r n

log sin

log tan

log COS

n f

t ft

log sin

log tan

log cos

9. 99 998

tt t

20

7.76475

7.76 476

9.99 999

4O

30

7. 94 084

7.94 086

3O

10

7.76 836

7. 76 837

9.99 999

50

10

7. 94 325

7. 94 326

9. 99 998

50

20

7. 77 193

7. 77 194

9.99 999

40

20

7. 94 564

7. 94 566

9. 99 998

40

30

7. 77 548

7. 77 549

9.99 999

30

30

7. 94 802

7. 94 804

9. 99 998

30

40

7. 77 899

7. 77 900

9.99 999

20

40

7. 95 039

7. 95 040

9. 99 998

20

SO

7. 78 248

7. 78 249

9.99 999

10

50

7. 95 274

7. 95 276

9.99 998

10

210

7. 78 594

7. 78 595

9.99 999

39

310

7. 95 508

7.95 510

9. 99 998

29

10

7. 78 938

7. 78 938

9.99 999

50

10

7. 95 741

7. 95 743

9. 99 998

50

20

7. 79 278

7. 79 279

9.99 999

40

20

7. 95 973

7. 95 974

9.99 998

40

30

7. 79 616

7.79 617

9.99 999

30

30

7. 96 203

7. 96 205

9. 99 998

30

40

7. 79 952

7. 79 952

9.99 999

20

40

7. 96 432

7.96 434

9.99 998

20

50

7. 80 284

7. 80 285

9.99 999

10

50

7. 96 660

7.96 662

9. 99 998

10

220

7. 80 615

7. SO 615

9.99 999

38

32

7. 96 887

7. 96 889

9. 99 998

28

10

7.80 942

7. 80 943

9.99 999

50

10

7. 97 113

7.97 114

9. 99 998

50

20

7. 81 268

7. 81 269

9. 99 999

40

20

7. 97 337

7. 97 339

9. 99 998

40

30

7. 81 591

7.81591

9.99 999

30

30

7. 97 560

7. 97 562

9. 99 998

30

40

7.81911

7.81912

9. 99 999

20

40

7. 97 782

7. 97 784

9. 99 998

20

50

7. 82 229

7. 82 230

9.99 999

10

50

7. 98 003

7. 98 005

9. 99 998

10

230

7. 82 545

7. 82 546

9.99 999

37

33

7. 98 223

7. 98 225

9. 99 998

27

10

7. 82 859

7. 82 860

9. 99 999

50

10

7. 98 442

7. 98 444

9. 99 998

50

20

7. 83 170

7. 83 171

9.99 999

40

20

7. 98 660

7. 98 662

9.99 998

40

30

7. 83 479

7. 83 480

9. 99 999

30

30

7. 98 876

7. 98 878

9. 99 998

30

40

7. 83 786

7. 83 787

9. 99 999

20

40

7. 99 092

7. 99 094

9. 99 998

20

50

7. 84 091

7. 84 092

9.99 999

10

50

7. 99 306

7. 99 308

9. 99 998

10

240

7. 84 393

7. 84 394

9.99 999

36

34

7. 99 520

7. 99 522

9. 99 998

26

10

7. 84 694

7. 84 695

9.99 999

50

10

7. 99 732

7. 99 734

9. 99 998

50

20

7. 84 992

7. 84 994

9. 99 999

40

20

7. 99 943

7. 99 946

9. 99 998

40

30

7. 85 289

7. 85 290

9. 99 999

30

30

8.00154

8.00156

9. 99 998

30

40

7. 85 583

7. 85 584

9.99 999

20

40

8. 00 363

8. 00 365

9.99 998

20

50

7. 85 876

7. 85 877

9. 99 999

10

50

8.00 571

8. 00 574

9. 99 998

10

260

7. 86 166

7. 86 167

9. 99 999

35

35

8. 00 779

8. 00 781

9. 99 998

25

10

7.86 455

7. 86 456

9.99 999

50

10

8. 00 985

8. 00 987

9. 99 998

50

20

7. 86 741

7. 86 743

9. 99 999

40

20

8. 01 190

8. 01 193

9. 99 998

40

30

7. 87 026

7. 87 027

9. 99 999

30

30

8. 01 395

8. 01 397

9. 99 998

30

40

7. 87 309

7.87 310

9.99 999

20

40

8. 01 598

8. 01 600

9. 99 998

20

50

7. 87 590

7. 87 591

9. 99 999

10

50

8. 01 801

8. 01 803

9. 99 998

10

260

7. 87 870

7. 87 871

9. 99 999

34

36

8. 02 002

8. 02 004

9. 99 998

24

10

7. 88 147

7. 88 148

9. 99 999

50

10

8. 02 203

8. 02 205

9. 99 998

50

20

7. 88 423

7. 88 424

9.99 999

40

20

8. 02 402

8. 02 405

9. 99 998

40

30

7. 88 697

7. 88 698

9.99 999

30

30

8. 02 601

8. 02 604

9. 99 998

30

40

7. 88 969

7. 88 970

9. 99 999

20

40

8. 02 799

8. 02 801

9. 99 998

20

50

7. 89 240

7. 89 241

9. 99 999

10

50

8. 02 996

8. 02 998

9. 99 998

10

270

7. 89 509

7.89 510

9. 99 999

33

37

8. 03 192

8. 03 194

9. 99 997

23

10

7. 89 776

7. 89 777

9. 99 999

50

10

8. 03 387

8. 03 390

9. 99 997

50

20

7.90 041

7.90 043

9. 99 999

40

20

8. 03 581

8. 03 584

9. 99 997

40

30

7. 90 305

7. 90 307

9.99 999

30

30

8. 03 775

8. 03 777

9. 99 997

30

40

7. 90 568

7. 90 569

9. 99 999

20

40

8. 03 967

8. 03 970

9. 99 997

20

SO

7. 90 829

7. 90 830

9.99 999

10

50

8. 04 159

8. 04 162

9. 99 997

10

280

7. 91 088

7. 91 089

9. 99 999

32

38

8. 04 350

8. 04 353

9. 99 997

22

10

7. 91 346

7. 91 347

9.99 999

50

10

8. 04 540

8. 04 543

9. 99 997

50

20

7. 91 602

7. 91 603

9.99 999

40

20

8. 04 729

8. 04 732

9. 99 997

40

30

7.91857

7. 91 858

9.99 999

30

30

8.04 918

8.04 921

9. 99 997

30

40

7.92 110

7.92 111

9.99 998

20

40

8. 05 105

8. 05 108

9. 99 997

20

50

7. 92 362

7. 92 363

9. 99 998

10

50

8. 05 292

8. 05 295

9. 99 997

10

290

7.92 612

7. 92 613

9. 99 998

031

39

8. 05 478

8. 05 481

9. 99 997

21

10

7. 92 861

7. 92 862

9.99 998

50

10

8. 05 663

8. 05 666

9. 99 997

50

20

7. 93 108

7.93 110

9. 99 998

40

20

8. 05 848

8.05 851

9. 99 997

40

30

7. 93 354

7. 93 356

9. 99 998

30

30

8.06 031

8. 06 034

9. 99 997

30

40

7. 93 599

7. 93 601

9. 99 998

20

40

8. 06 214

8.06 217

9. 99 997

20

SO

7. 93 842

7. 93 844

9. 99 998

10

50

8. 06 396

8. 06 399

9. 99 997

10

30

7. 94 084

7. 94 086

9. 99 998

3O

40

8. 06 578

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19

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18 932

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18

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8

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82 637

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6

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2

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37

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2

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t

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44

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42

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25 652

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34

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33

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32

29

25 995

26 726

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31

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26 063

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30

31

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26 867

73 133

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29

32

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26 937

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28

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27 008

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27

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26 335

27 078

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26

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72 852

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25

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26 470

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72 782

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24

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22

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26 672

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72 573

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21

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26 739

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20

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26 806

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19

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26 873

27 635

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18

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26 940

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17

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27 007

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16

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72 089

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14

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6

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4

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3

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2

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log oos

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t

m

w

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f

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f

9

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59

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58

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55

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28 769

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28 833

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48

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28 896

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28 960

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46

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29 024

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45

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29 087

29 932

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44

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43

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29 214

30 064

69 936

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42

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29 277

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69 870

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41

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40

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29 591

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29 716

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32

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31

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30

31

30 028

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69 089

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29

32

30 090

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28

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68 960

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27

34

30 213

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68 896

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26

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30 27i

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68 832

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25

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30 336

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68 767

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24

37

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23

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30 459

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68 639

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22

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30 521

31425

68 575

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30 582

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68 511

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20

41

30 643

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68 448

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19

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30 704

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68 384

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18

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30 765

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68 321

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17

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30 826

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30 887

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30 947

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68 067

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68 004

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32 059

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67 878

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32 185

67 815

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32 248

67 752

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67 689

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67 627

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6

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67 564

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6

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4

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3

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32 623

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2

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32 685

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1

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32 747

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9

log 008

9

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10

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9

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t

t

12°

88

t

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log oot

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t

9

9

10

9

31788

32 747

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60

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31847

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59

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32 872

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58

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66 881

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54

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32 670

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32 728

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32 786

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18

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14

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6

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3

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2

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39 623

60 377

98 694

1

60

38368

39 677

60 323

98 690

9

log COS

9

log oot

10

log tan

9

log tin

f

'

14^

f

log sin

log tan

log oot

log 008

/

9

38 368

9

39 677

10

60 323

9

98 690

60

1

38 418

39 731

60 269

98 687

59

2

38 469

39 785

60 215

98 684

58

3

38 519

39 838

60162

98 681

57

4

38 570

39 892

60108

98 678

56

5

38 620

39 945

60 055

98 675

55

6

38 670

39 999

60 001

98 671

54

7

38 721

40 052

59 948

98 668

53

8

38 771

40106

59 894

98 665

52

9

38 821

40159

59 841

98 662

51

10

38 871

40 212

59 788

98 659

50

11

38 921

40 266

59 734

98 656

49

12

38971

40 319

59 681

98 652

48

13

39 021

40 372

59 628

98 649

47

14

39 071

40 425

59 575

98 646

46

15

39121

40 478

59 522

98 643

45

16

39170

40 531

59 469

98 640

44

17

39 220

40 584

59 416

98 636

43

18

39 270

40 636

59 364

98 633

42

19

39 319

40 689

59 311

98 630

41

20

39 369

40 742

59 258

98 627

40

21

39 418

40 795

59 205

98 623

39

22

39 467

•10 847

59 153

98 620

38

23

39 517

40 900

59 100

98 617

3.7

24

39 566

40 952

59 048

98 614

36

25

39 615

41005

58 995

98 610

35

26

39 664

41057

58 943

98 607

34

27

39 713

41109

58 891

98 604

33

28

39 762

41161

58 839

98 601

32

29

39 811

41214

58 786

98 597

31

30

39 860

41266

58 734

98 594

30

31

39 909

41318

58 682

98 591

29

32

39 958

41370

58 630

98 588

28

33

40006

41422

58 578

98 584

27

34

40 055

41474

58 526

98 581

26

35

40103

41526

58 474

98 578

25

36

40152

41578

58 422

98 574

24

37

40 200

41629

58 371

98 571

23

38

40 249

41681

58 319

98 568

22

39

40 297

41733

58 267

98 565

21

40

40 346

41784

58 216

98 561

20

41

40 394

41836

58164

98 558

19

42

40442

41887

58113

98 555

18

43

40 490

41939

58 061

98 551

17

44

40 538

41990

58 010

98 548

16

45

40 586

42 041

57 959

98 545

15

46

40 634

42 093

57 907

98 541

14

47

40 682

42144

57 856

98 538

13

48

40 730

42 195

57 805

98 535

12

49

40 778

42 246

57 754

98 531

11

50

40 825

42 297

57 703

98 528

10

51

40 873

42 348

57 652

■98 525

9

52

40 921

42 399

57 601

98 521

8

53

40 968

42 450

57 550

98 518

7

54

41016

42 501

57 499

98 515

6

55

41063

42 552

57 448

98 511

5

56

41111

42 603

57 397

98 508

4

.57

41158

42 653

57 347

98 505

3

58

412C5

42 704

57 296

98 501

2

59

41252

42 755

57 245

98 498

1

60

41300

42 805

57195

98494

9

9

10

9

t

log 00 s

log oot

log tan

log sin

r

76<

76=

16'

t

log sin

log tan

log cot

log 008

t

9

41300

9

42 805

lO

57195

9

98 494

o

60

1

41347

42 856

57144

98 491

59

2

41394

42 906

57 094

98 488

58

3

41441

42 957

57 043

98 484

57

4

41488

43 007

56 993

98 481

56

5

41535

43 057

56 943

98 477

55

6

41582

43 108

56 892

98 474

54

7

41628

43 158

56 842

98 471

53

8

41675

43 208

56 792

98 467

52

9

41722

43 258

56 742

98 464

51

10

41768

43 308

56 692

98 460

50

11

41815

43 358

56 642

98 457

49

12

41861

43 408

56 592

98 453

48

13

41908

43 458

56 542

98 450

47

14

41954

43 508

56 492

98 447

46

15

42 001

43 558

56 442

98 443

45

16

42 047

43 607

56 393

98 440

44

17

42 093

43 657

56343

98 436

43

18

42140

43 707

56 293

98 433

42

19

42186

43 756

56 244

98 429

41

20

42 232

43 806

56194

98 426

40

21

42 278

43 855

56145

98 422

39

22

42 324

43 905

56 095

98 419

38

23

42 370

43 954

56 046

98 415

37

24

42 416

44 004

55 996

98 412

36

25

42 461

44 053

55 947

98 409

35

26

42 507

44102

55 898

98 405

34

27

42 553

44 151

55 849

98 402

33

28

42 599

44 201

55 799

98 39S

32

29

42 644

44 250

55 750

98 395

31

30

42 690

44 299

55 701

98 391

30

31

42 735

44 348

55 652

98 388

29

32

42 781

44 397

55 603

98 384

28

33

42 826

44 446

55 554

98 381

27

34

42 872

44 495

55 505

98 377

26

35

42917

44 544

55 456

98 373

25

36

42 962

44 592

55 408

98 370

24

37

43 008

44 641

55 359

98 366

23

38

43 053

44 690

55 310

98 363

22

39

43 098

44 738

55 262

98 359

21

40

43 143

44 787

55 213

98 356

20

41

43 188

44 836

55 164

98 352

19

42

43 233

44 884

55 116

98 349

18

43

43 278

44 933

55 067

98 345

17

44

43 323

44 981

55 019

98 342

16

45

43 367

45 029

54 971

98 338

15

46

43 412

45 078

54 922

98 334

14

47

43 457

45 126

54 874

98 331

13

48

43 502

45 174

54 826

98 327

12

49

43 546

45 222

54 778

98 324

11

50

43 591

45 271

54 729

98 320

10

51

43 635

45 319

54 681

98 317

9

52

43 680

45 367

54 633

98 313

8

53

43 724

45 415

54 585

98 309

7

54

43 769

45 463

54 537

98 306

6

55

43 813

45 511

54 489

98 302

5

56

43 857

45 559

54 441

98 299

4

57

43 901

45 606

54 394

98 295

3

58

43 946

45 654

54 346

98 291

2

59

43 990

45 702

54 298

98 288

1

60

44 034

45 750

54 250

98 284

O

9

log COS

9

log cot

lO

log tan

9

log sin

f

t

16°

35

t

log sin

log tan

log Got

log 008

t

9

44 034

9

45 7i0

10

54 250

9

98 284

60

1

44 078

45 797

54 203

98 281

59

2

44122

45 84i

54155

98 277

58

3

44 166

45 892

54108

98 273

57

4

44 210

45 940

54 060

98 270

56

5

44 253

45 987

54 013

98 266

65

6

44 297

46 035

53 965

98 262

54

7

44 341

46 082

53 918

98 259

53

8

44 385

46130

53 870

98 255

52

9

44 428

46177

53 823

98 251

51

10

44 472

46 224

53 776

98 248

50

11

44 516

46 271

53 729

98 244

49

12

44 559

46 319

53 681

98 240

48

13

44 602

46 366

53 634

98 237

47

14

44 646

46 413

53 587

98 233

46

15

44 689

46 460

53 540

98 229

45

16

44 733

46 507

53 493

98 226

44

17

44 776

46 554

53 446

98 222

43

18

44 819

46 601

53 399

98 218

42

19

44 862

46 648

53 352

98 215

41

20

44 905

46 694

53 306

98 211

40

21

44 948

46 741

53 259

98 207

39

22

44 992

46 788

53 212

98 204

38

23

45 035

46 835

53165

98 200

37

24

45 077

46 881

53 119

98196

36

25

45 120

46 928

53 072

98192

35

26

45 163

46 975

53 025

98189

34

27

45 206

47 021

52 979

98185

3,2,

28

45 249

47 068

52 932

98 181

32

29

45 292

47114

52 886

98177

31

30

45 334

47 160

52 840

98174

30

31

45 377

47 207

52 793

98170

29

32

45 419

47 253

52 747

98166

28

33

45 462

47 299

52 701

98162

27

34

45 504

47 346

52 654

98 159

26

35

45 547

47 392

52 608

98 155

25

36

45 589

47 438

52 562

98 151

24

37

45 632

47 484

52 516

98147

23

38

45 674

47 530

52 470

98144

22

39

45 716

47 576

52 424

98140

21

40

45 758

47 622

52 378

98136

20

41

45 801

47 668

52 332

98132

19

42

45 843

47 714

52 286

98129

18

43

45 885

47 760

52 240

98125

17

44

45 927

47 806

52 194

98121

16

45

45 969

47 852

52 148

98117

15

46

46 011

47 897

52 103

98113

14

47

46 053

47 943

52 057

98110

13

48

46 095

47 989

52 011

98106

12

49

46136

48 035

51965

98102

11

50

46178

48 080

51920

98 098

10

51

46 220

48126

51874

98 09+

9

52

46 262

48171

51829

98 090

8

53

46 303

48 217

51783

98 087

7

54

46 345

48 262

51738

98 083

6

55

46 386

48 307

51693

98 079

5

56

46 428

48 353

51647

98 075

4

57

46 469

48 398

51602

98 071

3

58

46 511

48 443

51557

98 067

2

59

46 552

48 489

51511

98 063

1

60

46 594

48 534

51466

98 060

O

9

9

lO

9

f

log 008

log cot

log tan

log sin

t

74c

73'

36

17°

t

log sin

log tan

log oot

log 008

t

9

46 594

9

48 534

10

51466

9

98 060

O

60

1

46 635

48 579

51421

98 056

59

2

46676

48 624

51376

98052

58

3

46 717

48 669

51331

98 048

57

4

46 758

48 714

51286

98 044

56

5

46 800

48 759

51241

98 040

56

6

46 841

48 804

51196

98 036

54

7

46 882

48 849

51151

98 032

53

8

46 923

48 894

51106

98 029

52

9

46 964

48 939

51061

98 025

51

10

47 005

48 984

51016

98 021

50

11

47 045

49 029

50 971

98 017

49

12

47 086

49 073

50 927

98 013

48

13

47 127

49118

50 882

98 009

47

14

47168

49163

50 837

98 005

46

15

47 209

49 207

50 793

98 001

45

16

47 249

49 252

50 748

97 997

44

17

47 290

49 296

50 704

97 993

43

18

47 330

49 341

50 659

97 989

42

19

47 371

49 385

50 615

97 986

41

20

47 411

49 430

50 570

97 982

40

21

47 452

49 474

50 526

97 978

39

22

47 492

49 519

50 481

97 974

38

23

47 533

49 563

50 437

97 970

37

24

47 573

49 607

50 393

97 966

36

25

47 613

49 652

50 348

97 962

35

26

47 654

49 696

50 304

97 958

34

27

47 694

49 740

50 260

97 954

2>i

28

47 734

49 784

50 216

97 950

32

29

47 774

49 828

50172

97 946

31

30

47 814

49 872

50128

97 942

30

31

47 854

49 916

50 084

97 938

29

32

47 894

49 960

50 040

97 934

28

33

47 934

50 004

49 996

97 930

27

34

47 974

50 048

49 952

97 926

26

35

48 014

50 092

49 908

97 922

25

36

48 054

50136

49 864

97 918

24

37

48 094

50180

49 820

97 914

23

38

48133

50 223

49 777

97 910

22

39

48173

50 267

49 733

97 906

21

40

48 213

50 311

49 689

97 902

20

41

48 252

50355

49 645

97 898

19

42

48 292

50 398

49 602

97 894

18

43

48 332

50 442

49 558

97 890

17

44

48 371

50 485

49 515

97 886

16

45

48 411

50 529

49 471

97 882

15

46

48 450

50 572

49 428

97 878

14

47

48 490

50 616

49 384

97 874

13

48

48 529

50 659

49 341

97 870

12

49

48 568

50 703

49 297

97 866

11

50

48 607

50 746

49 254

97 861

10

51

48 647

50 789

49 211

97 857

9

52

48 686

50 833

49167

97 853

8

53

48 725

50 876

49124

97 849

7

54

48 764

50 919

49 081

97 845

6

55

48 803

50 962

49 038

97 841

5

56

48 842

51005

48 995

97 837

4

57

48 881

51048

48 952

97 833

3

58

48920

51092

48 908

97 829

2

59

48 959

51135

48 865

97 825

1

«o

48 998

51178

48 822

97 821

O

9

log 008

9

log oot

10

Q

t

log tan

log sin

t

18°

t

log sin

log tan

log cot

log cos

/

9

9

lO

9

o

48 998

51178

48 822

97 821

60

1

49 037

51221

48 779

97 817

59

2

49 076

51264

48 736

97 812

58

3

49 115

51306

48 694

97 808

57

4

49153

51349

48 651

97 804

56

5

49192

51392

48 608

97 800

55

6

49 231

51435

48 565

97 796

54

7

49 269

51478

48 522

97 792

53

8

49 308

51520

48 480

97 788

52

9

49 347

51563

48 437

97 784

51

lO

49 385

51606

48 394

97 779

50

11

49 424

51648

48 352

97 775

49

12

49 462

51691

48 309

97 771

48

13

49 500

51734

48 266

97 767

47

14

49 539

51776

48 224

97 763

46

15

49 577

51819

48181

97 759

45

16

49 615

51861

48139

97 754

44

17

49 654

51903

48 097

97 750

43

18

49 692

51946

48 054

97 746

42

19

49 730

51988

48 012

97 742

41

20

49 768

52 031

47 969

97 738

40

21

49 806

52 073

47 927

97 734

39

22

49 844

52 115

47 885

97 729

38

23

49 882

52 157

47 843

97 725

37

24

49 920

52 200

47 800

97 721

36

25

49 958

52 242

47 758

97 717

35

26

49 996

52 284

47 716

97 713

34

27

50 034

52 326

47 674

97 708

33

28

50 072

52 368

47 632

97 704

32

29

50110

52 410

47 590

97 700

31

30

50148

52 452

47 548

97 696

30

31

50185

52 494

47 506

97 691

29

32

50 223

52 536

47 464

97 687

28

33

50 261

52 578

47 422

97 683

27

34

50 298

52 620

47 380

97 679

26

35

50 336

52 661

47 339

97 674

25

36

50 374

52 703

47 297

97 670

24

37

50411

52 745

47 255

97 666

23

38

50 449

52 787

47 213

97 662

22

39

50 486

52 829

47 171

97 657

21

40

50 523

52 870

47 130

97 653

20

41

50 561

52 912

47 088

97 649

19

42

50 598

52 953

47 047

97 645

18

43

50 635

52 995

47 005

97 640

17

44

50 673

53 037

46 963

97 636

16

45

50 710

53 078

46 922

97 632

15

46

50 747

53 120

46 880

97 628

14

47

50 784

53 161

46 839

97 623

13

48

50 821

53 202

46 798

97 619

12

49

50 858

53 244

46 756

97 615

11

50

50 896

53 285

46 715

97 610

lO

51

50 933

53 327

46 673

97 606

9

52

50 970

53 368

46 632

97 602

8

• 53

51007

53 409

46 591

97 597

7

54

51043

53 450

46 550

97 593

6

55

51080

53 492

46 508

97 589

5

56

51117

53 533

46 467

97 584

4

57

51154

53 574

46 426

97 580

3

58

51191

53 615

46 385

97 576

2

59

51227

53 656

46 344

97 571

1

60

51264

53 697

46 303

97 567

O

9

9

lO

9

t

log 008

log oot

log tan

log sin

f

72'

n

19'

r

log sin

log tan

log oot

log 008

/

9

51264

9

53 697

lO

46 303

9

97 567

60

1

51301

53 738

46 262

97 563

59

2

51338

53 779

46 221

97 558

58

3

51 374

53 820

46180

97 554

57

4

51411

53 861

46139

97 5i0

56

5

51447

53 902

46 098

97 545

55

6

51484

53 943

46 057

97 541

54

7

51520

53 984

46 016

97 536

53

8

51557

54 025

45 975

97 532

52

9

51593

54 065

45 935

97 528

51

10

51629

54106

45 894

97 523

50

11

51666

54147

45 853

97 519

49

12

51702

54187

45 813

97 515

48

13

51738

54 228

45 772

97 510

47

14

51774

54 269

45 731

97 506

46

15

51811

54 309

45 691

97 501

45

16

51847

54 350

45 650

97 497

44

17

51883

54 390

45 610

97 492

43

18

51919

54 431

45 569

97 488

42

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19

42

62 104

66 271

33 729

95 833

18

43

62 131

66 304

33 696

,95 827

17

44

62159

66 337

33 663

95 821

16

45

62 186

66 371

33 629

95 815

15

46

62 214

66 404

33 596

95 810

14

47

62 241

66 437

33 563

95 804

13

48

62 268

66 470

33 530

95 798

12

49

62 296

66 503

33 497

95 792

11

50

62 323

66 537

33 463

95 786

10

51

62 350

66 570

33 430

95 780

9

52

62 377

66 603

33 397

95 77i

8

53

62 405

66 636

33 364

95 769

7

54

62 432

66 669

33 331

95 763

6

55

62 459

66 702

33 298

95 757

5

56

62 486

66 735

33 265

95 751

4

57

62 513

66 768

33 232

95 745

3

58

62 541

66 801

33 199

95 739

2

59

62 568

66 834

33 166

95 733

1

60

62 595

66 867

33 133

95 728

9

log cos

9

log cot

lO

log tan

9

log sin

t

f

66^

66=

40

25°

r

log sin

log tan

log cot

log COS

t

9

9

lO

9

O

62 595

66 867

33 133

95 728

60

1

62 622

66 900

33 100

95 722

59

2

62 649

66 933

33 067

95 716

58

3

62 676

66 966

33 034

95 710

57

4

62 703

66 999

33 001

95 704

56

5

62 730

67 032

32 968

95 698

55

6

62 757

67 065

32 935

95 692

54

7

62 784

67 098

32 902

95 686

53

8

62 811

67 131

32 869

95 680

52

9

62 838

67 163

32 837

95 674

51

10

62 865

67 196

32 8(H

95 668

60

11

62 892

67 229

32 771

95 663

49

12

62 918

67 262

32 738

95 657

48

13

62 945

67 295

32 705

95 651

47

14

62 972

67 327

32 673

95 645

46

15

62 999

67 360

32 640

95 639

45

16

63 026

67 393

32 607

95 633

44

17

63 052

67 426

32 574

95 627

43

18

63 079

67 458

32 542

95 621

42

19

63 106

67 491

32 509

95 615

41

20

63 133

67 524

32 476

95 609

40

21

63 159

67 556

32 444

95 603

39

22

63 186

67 589

32 411

95 597

38

23

63 213

67 622

32 378

95 591

37

24

63 239

67 654

32 346

95 585

36

25

63 266

67 687

32 313

95 579

35

26

63 292

67 719

32 281

95 573

34

27

63 319

67 752

32 248

95 567

33

28

63 345

67 785

32 215

95 561

32

29

63 372

67 817

32 183

95 555

31

30

63 398

67 850

32150

95 549

30

31

63 425

67 882

32118

95 543

29

32

63 451

67 915

32 085

95 537

28

33

63 478

67 947

32 053

95 531

27

34

63 504

67 980

32 020

95 525

26

35

63 531

68 012

31988

95 519

26

36

63 557

68 044

31956

95 513

24

^37

63 583

68 077

31923

95 507

23

38

63 610

68109

31891

95 500

22

39

63 636

68142

31858

95 494

21

40

63 662

6S174

31826

95 488

20

41

63 689

68 206

31794

95 482

19

42

63 715

68 239

31761

95 476

18

43

63 741

68 271

31729

95 470

17

44

63 767

68 303

31697

95 464

16

45

63 794

6S336

31664

95 458

15

46

63 820

68 368

31632

95 452

14

47

63 846

68 400

31600

95 446

13

48

63 872

68 432

31568

95 440

12

49

63 898

68 465

31535

95 434

11

60

63 924

68 497

31503

95 427

lO

51

63 950

68 529

31471

95 421

9

52

63 976

68 561

31439

95 415

8

53

64 002

68 593

31407

95 409

7

54

64 028

68 626

31374

95 403

6

65

64 054

68 658

31342

95 397

5

56

64 080

68 690

31310

95 391

4

57

64 106

68 722

31278

95 384

3

58

64 132

68 754

31246

95 378

2

59

64 158

68 786

31214

95 372

1

60

64184

68 818

31182

95 366

9

9

lO

9

f

log cos

log cot

log tan

log sin

f

26'

f

log sin

log tan

log cot

log COS

/

9

9

10

9

64 184

68 818

31182

95 366

60

1

64 210

68 850

31150

95 360

59

2

64 236

68 882

31118

95 354

58

3

64 262

68 914

31086

95 348

57

4

64 288

68 946

31 054

95 341

56

5

64 313

68 978

31022

95 335

56

6

64 339

69 010

30 990

95 329

54

7

64 365

69 042

30 958

95 323

53

8

64 391

69 074

30 926

95 317

52

9

64 417

69106

30 894

95 310

51

10

64 442

69138

30 862

95 304

50

11

64 468

69170

30 830

95 298

49

12

64 494

69 202

30 798

95 292

48

13

64 519

69 234

30 766

95 286

47

14

64 545

69 266

30 734

95 279

46

16

64 571

69 298

30 702

95 273

45

16

64 596

69 329

30 671

95 267

44

17

64 622

69 361

30 639

95 261

43

18

64 647

69 393

30 607

95 254

42

19

64 673

69 425

30 575

95 248

41

20

64 698

69 457

30 543

95 242

40

21

64 724

69 488

30 512

95 236

39

22

64 749

69 520

30 480

95 229

38

23

64 775

69 552

30 448

95 223

37

24

64 800

69 584

30 416

95 217

36

25

64 826

•69 615

30 385

95 211

36

26

64 851

69 647

30 353

95 204

34

27

64 877

69 679

30 321

95 198

33

28

64 902

69 710

30 290

95 192

32

29

64 927

69 742

30 258

95 185

31

30

64 953

69 774

30 226

95 179

30

31

64 978

69 805

30195

95 173

29

32

65 003

69 837

30163

95 167

28

33

65 029

69 868

30132

95 160

27

34

65 054

69 900

30100

95 154

26

35

65 079

69 932

30 068

95 148

26

36

65 104

69 963

30 037

95 141

24

37

65 130

69 995

30 005

95 135

23

38

65 155

70 026

29 974

95 129

22

39

65 180

70 058

29 942

95 122

21

40

65 205

70 089

29 911

95 116

20

41

65 230

70121

29 879

95 110

19

42

65 255

70152

29 848

95 103

18

43

65 281

70184

29 816

95 097

17

44

65 306

70 215

29 785

95 090

16

45

65 331

70 247

29 753

95 084

16

46

65 356

70 278

29 722

95 078

14

47

65 381

70 309

29 691

95 071

13

48

65 406

70 341

29 659

95 065

12

49

65 431

70 372

29 628

95 059

11

60

65 456

70 404

29 596

95 052

10

51

65 481

70 435

29 565

95 046

9

52

65 506

70 466

29 534

95 039

8

53

65 531

70 498

29 502

95 033

7

54

65 556

70 529

29 471

95 027

6

65

65 580

70 560

29 440

95 020

5

56

65 605

70 592

29 408

95 014

4

57

65 630

70 623

29 377

95 007

3

58

65 655

70654

29 346

95 001

2

59

65 680

70 685

29 315

94 995

1

60

65 705

70 717

29 283

94 988

9

9

lO

9

f

log cos

log cot

log tan

log sin

f

64'

63'

27

O

1
2
3
4

6

6

7
8
9

lO

11
12
13
14

15

16
17
18
19

20

21
22
23
24

25

26
27
28
29
30
31
32
33
34

35

36
37
38
39

40

41
42
43
44

45

46
47
48
49
50
51
52
53
54

55

56
57
58
59
60

log sin

9
65 705
65 729
65 754
65 779
65 804
65 828
65 853
65 878
65 902
65 927
65 952

65 976

66 001
66 025
66 050
66 075
66 099
66124
66 148
66173

66197
66 221
66 246
66 270
66 295
66 319
66 343
66 368
66 392
66 416
66 441
66465
66 489
66 513
66 537
66 562
66 586
66 610
66 634
66 658
66 682
66 706
66 731
66 755
66 779
66 803
66 827
66 851
66 875
66 899
66 922
66 946
66 970

66 994

67 018
67 042
67 066
67 090
67 113
67 137
67161

9
log cos

log tan

9
70 717
70 748
70 779
70 810
70 841
70 873
70 904
70 935
70 966
70 997
71028
71059
71090
71121
71153
71184
71215
71246
71277
71308
71339
71370
71401
71431
71462
71493
71524
71555
71586
71617
71648
71679
71709
71740
71771
71802
71833
71863
71894
71925
71955
71986
72 017
72 048
72 078
72109
72 140
72 170
72 201
72 231
72 262
72 293
72 323
72 354
72 384
72 415
72 445
72 476
72 506
72 537
72 567

9
leg cot

log cot
lO

29 283
29 252
29 221
29190
29159
29127
29 096
29 065
29 034
29 003
28 972
28 941
28 910
28 879
28 847
28 816
28 785
28 754
28 723
28 692
28 661
28 630
28 599
28 569
28 538
28 507
28 476
28 445
28 414
28 383
28 352
28 321
28 291
28 260
28 229
28 198
28167
28137
28106
28 075
28 045
28 014
27 983
27 952
27 922
27 891
27 860
27 830
27 799
27 769
27 738
27 707
27 677
27 646
27 616
27 585
27 555
27 524
27 494
27 463
27 433
lO
log tan

log COS

9

94 988
94 982
94 975
94 969
94 962
94 956
94 949
94 943
94 936
94 930
94 923
94 917
94 911
94 904
94 898
94 891
94 885
94 878
94 871
94 865
94 858
94 852
94 845
94 839
94 832
94 826
94 819
94 813
94 806
94 799
94 793
94 786
94 780
94 773
94 767
94 760
94 753
94 747
94 740
94 734
94 727
94 720
94 714
94 707
94 700
94 694
94 687
94 680
94 674
94 667
94 660
94 654
94 647
94 640
94 634
94 627
94 620
94 614
94 607
94 600
94 593

9
log sin

60

59
58
57
56
55
54
53
52
51
50
49
48
47
46

45

44
43
42
41
40
39
38
37
36

35

34
33
32
31
30
29
28
27
26

25

24
23
22
21

20

19
18
17
16

15

14

13
12
11

10

9
8
7
6

5

4
3
2
1

O

28°

41

f

logiin

log tan

log oot

log cos

f

9

9

lO

9

67161

72 567

27 433

94 593

60

1

67 185

72 598

27 402

94 587

59

2

67 208

72 628

27 372

94 580

58

3

67 232

72 659

27 341

94 573

57

4

67 256

72 689

27 311

94 567

56

5

67 280

72 720

27 280

94 560

55

6

67 303

72 750

27 250

94 553

54

7

67 327

72 780

27 220

94 546

53

8

67 350

72 811

27 189

94 540

52

9

67 374

72 841

27159

94 533

51

10

67 398

72 872

27128

94 526

50

11

67 421

72 902

27 098

94 519

49

12

67 445

72 932

27 068

94 513

48

13

67 468

72 963

27 037

94 506

47

14

67 492

72 993

27 007

94 499

46

15

67 515

73 023

26 977

94 492

45

16

67 539

73 054

26 946

94 485

44

17

67 562

73 084

26 916

26 88»

94 479

43

18

67 586

73 114

94 472

42

19

67 609

73 144

26 856

94 465

41

20

67 633

73 175

26 825

94 458

40

21

67 656

73 205

26 795

94 451

39

22

67 680

73 235

26 765

94 445

38

23

67 703

73 265

26 735

94 438

37

24

67 726

73 295

26 705

94 431

36

25

67 750

73 326

26 674

94 424

35

26

67 773

73 356

26 644

94 417

34

27

67 796

73 386

26 614

94 410

33

28

67 820

73 416

26 584

94 404

32

29

67 843

73 446

26 554

94 397

31

30

67 866

73 476

26 524

94 390

30

31

67 890

73 507

26 493

94 383

29

32

67 913

73 537

26 463

94 376

28

33

67 936

73 567

26 433

94 369

27

34

67 959

73 597

26 403

94 362

26

35

67 982

73 627

26 373

94 355

25

36

68 006

73 657

26 343

94 349

24

37

68 029

73 687

26 313

94 342

23

38

68 052

73 717

26 283

94 335

22

39

68 075

73 747

26 253

94 328

21

40

68 098

73 777

26 223

94 321

20

41

68121

73 807

26193

94 314

19

42

68 144

73 837

26163

94 307

18

43

68 167

73 867

26133

94 300

17

44

68190

73 897

26103

94 293

16

45

68 213

73 927

26 073

94 286

15

46

68 237

73 957

26 043

94 279

14

47

68 260

73 987

26 013

94 273

13

48

68 283

74 017

25 983

94 266

12

49

68 305

74 047

25 953

94 259

11

50

68 328

74 077

25 923

94 252

10

51

68 351

74 107

25 893

94 245

9

52

68 374

74 137

25 863

94 238

8

53

68 397

74 166

25 834

94 231

7

54

68 420

74 196

25 804

94 224

6

55

68 443

74 226

25 774

94 217

5

56

68 466

74 256

25 744

94 210

4

57

68 489

74 286

25 714

94 203

3

58

68 512

74 316

25 684

94 196

2

59

68 534

74 345

25 655

94189

1

60

68 557

74 375

25 625

94182

9

9

lO

9

f

log cos

log oot

log tan

log sin

t

68P

61'

42

29°

t

log sin

log tan

log cot

log oos

f

9

68 557

9

74 375

10

25 625

9

94 182

60

1

68 580

74 405

25 595

94 175

59

2

68 603

74 435

25 565

94 168

58

3

68 625

74 465

25 535

94 161

57

4

68 648

74 494

25 506

94 154

56

5

68 671

74 524

25 476

94147

55

6

68 694

74 554

25 446

94 140

54

7

68 716

74 583

25 417

94133

53

8

68 739

74 613

25 387

94 126

52

9

68 762

74 643

25 357

94 119

51

lO

68 784

74 673

25 327

94112

50

11

68 807

74 702

25 298

94 105

49

12

68 829

74 732

25 268

94 098

48

13

68 852

74 762

25 238

94 090

47

14

68 875

74 791

25 209

94 083

46

15

68 897

74 821

25 179

94 076

45

16

68 920

74 851

25 149

94 069

44

17

68 942 #74 880

25 120

94 062

43

18

68 965

74 910

25 090

94 055

42

19

68 987

74 939

25 061

94 04S

41

20

69 010

74 969

25 031

94 041

40

21

69 032

74 998

25 002

94 034

39

22

69 055

75 028

24 972

94 027

38

11

69 077

75 058

24 942

94 020

37

24

69100

75 087

24 913

94 012

36

25

69122

75 117

24 883

94 005

35

26

69144

75 146

24 854

93 998

34

27

69167

75 176

24 824

93 991

33

28

69189

75 205

24 795

93 984

32

29

69 212

75 235

24 765

93 977

31

30

69 234

75 264

24 736

93 970

30

31

69 256

75 294

24 706

93 963

29

32

69 279

75 323

24 677

93 955

28

33

69 301

75 353

24 647

93 948

27

34

69 323

75J82

24 618

93 941

26

35

69 345

75 411

24 589

93 934

25

36

69 368

75 441

24 559

93 927

24

37

69 390

75 470

24 530

93 920

23

38

69 412

75 500

24 500

93 912

22

39

69 434

75 529

24 471

93 905

21

40

69 456

75 558

24 442

93 898

20

41

69 479

75 588

24 412

93 891

19

42

69 501

75 617

24 383

93 884

18

43

69 523

75 647

24 353

93 876

17

44

69 545

75 676

24 324

93 869

16

45

69 567

75 705

24 295

93 862

15

46

69 589

75 735

24 265

93 855

14

47

69 611

75 764

24 236

93 847

13

48

69 633

75 793

24 207

93 840

12

49

69 655

75 822

24 178

93 833

11

50

69 577

75 852

24 148

93 826

10

51

69 699

75 881

24 119

93 819

9

52

69 721

75 910

24 090

93 811

8

53

69 743

75 939

24 061

93 804

7

54

69 765

75 969

24 031

93 797

6

55

69 787

75 998

24 002

93 789

5

56

69 809

76 027

23 973

93 782

4

57

69 831

76 056

23 944

93 775

3

58

69 853

76 086

23 914

93 768

2

59

69 875

76115

23 885

93 760

1

60

69 897

76144

23 856

93 753

9

9

10

9

f

logooa

log oot

log tan

log sin

f

30^

f

log sin

log tan

log oot

log cos

/

9

69 897

9

76144

10

23 856

9

93 753

60

1

69 919

76173

23 827

93 746

59

2

69 941

76 202

23 798

93 738

58

3

69 963

76 231

23 769

93 731

57

4

69 984

76 261

23 739

93 724

56

5

70 006

76 290

23 710

93 717

55

6

70 028

76 319

23 681

93 709

54

7

70 050

76 348

23 652

93 702

53

8

70 072

76 377

23 623

93 695

52

9

70 093

76 406

23 594

93 687

51

10

70115

76 435

23 565

93 680

50

11

70137

76 464

23 536

93 673

49

12

70159

76 493

23 507

93 665

48

13

70180

76 522

23 478

93 658

47

14

70 202

76 551

23 449

93 650

46

15

70 224

76 580

23 420

93 643

45

16

70 245

76 609

23 391

93 636

44

17

70 267

76 639

23 361

93 628

43

18

70 288

76 668

23 332

93 621

42

19

70 310

76 697

23 303

93 614

41

20

70 332

76 725

23 275

93 606

40

21

70 353

76 754

23 246

93 599

39

22

70 375

76 783

23 217

93 591

38

23

70 396

76 812

23 188

93 584

37

24

70 418

76 841

23 159

93 577

36

25

70 439

76 870

23 130

93 569

35

26

70 461

76 899

23 101

93 562

34

27

70 482

76 928

23 072

93 554

33

28

70 504

76 957

23 043

93 547

32

29

70 525

76 986

23 014

93 539

31

30

70 547^
70 568-

) 77 015

22 985

93 532

30

31

77 044

22 956

93 525

29

32

70 590

77 073

22 927

93 517

28

ZZ

70 611

77101

22 899

93 510

27

34

70 633

77130

22 870

93 502

26

35

70 654

77 159

22 841

93 495

25

36

70 675

77188

22 812

93 487

24

37

70 697

77 217

22 783

93 480

23

38

70 718

77 246

22 754

93 472

22

39

70 739

77 274

22 726

93 465

21

40

70 761

77 303

22 697

93 457

20

41

70 782

77 332

22 668

93 450

19

42

70 803

77 361

22 639

93 442

18

43

70 824

77 390

22 610

93 435

17

44

70 846

77 418

22 582

93 427

16

45

70 867

77 447

22 553

93 420

15

46

70G88

77 47o

22 524

93 412

14

47

70 909

77 505

22 495

93 405

13

48

70 931

77 533

22 467

93 397

12

49

70 952

77 562

22 438

93 390

11

50

70 973

77 591

22 409

93 382

10

51

70 994

77 619

22 381

93 375

9

52

71015

77 648

22 352

93 367

8

53

71036

77 677

22 323

93 360

7

54

71 058

77 706

22 294

93 352

6

55

71079

77 734

22 266

93 344

5

56

71100

77 763

22 237

93 337

4

57

71121

77 791

22 209

93 329

3

58

71142

77 820

22 180

93 322

2

59

71163

77 849

22 151

93 314

1

60

71184

77 877

22 123

93 307

9

log OOB

9

log oot

lO

log tan

9

log sin

t

f

m

m

sv

r

log sin

log tan

log cot

log 008

t

9

71184

9

77 877

lO

22123

9

93 307

O

60

1

71205

77 906

22 094

93 299

59

2

71226

77 935

22 065

93 291

58

3

71247

77 963

22 037

93 284

57

4

71268

77 992

22 008

93 276

56

6

71289

78 020

21980

93 269

55

6

71310

78 049

21951

93 261

54

7

71331

78 077

21923

93 253

53

8

71352

78106

21894

93 246

52

9

71373

78 135

21865

93 238

51

lO

71393

78163

21837

93 230

50

11

71414

78192

21808

93 223

49

12

71435

78 220

21780

93 215

48

13

71456

78 249

21751

93 207

47

14

71477

78 277

21723

93 200

46

15

71498

78 306

21694

93 192

45

16

71 519

78 334

21666

93 184

44

17

71539

78 363

21637

93177

43

18

71560

78 391

21609

93169

42

19

71581

78 419

21581

93161

41

20

71602

78 448

21552

93154

40

21

71622

78 476

21524

93146

39

22

71643

78 505

21495

93138

38

23

71664

78 533

21467

93 131

37

24

71685

78 562

21438

93123

36

25

71705

78 590

21410

93 115

35

26

71726

78 618

21382

93 108

34

27

71747

78 647

21353

93100

33

28

71767

78 675

21325

93 092

32

29

71788

78 704

21296

93 084

31

30

71809

78 732

21268

93 077

30

31

71829

78 760

21240

93 069

29

32

71850

78 789

21211

93 061

28

33

71870

78 817

21183

93 053

27

34

71891

78 845

21155

93 046

26

35

71911

78 874

21126

93 038

25

36

71932

78 902

21098

93 030

24

37

71952

78 930

21070

93 022

23

38

71973

78 959

21041

93 014

22

39

71994

78987

21013

93 007

21

40

72 014

79 015

20 985

92 999

20

41

72 034

79 043

20 957

92 991

19

42

72 055

79 072

20 928

92 983

18

43

72 075

79100

20 900

92 976

17

44

72 096

79 128

20 872

92 968

16

45

72116

79156

20 844

92 960

15

46

72137

79185

20 815

92 952

14

47

72157

79 213

20 787

92 944

13

48

72177

79 241

20 759

92 936

12

49

72198

79 269

20 731

92 929

11

50

72 218

79 297

20 703

92 921

lO

51

72 238

79 326

20 674

92 913

9

52

72 259

79 354

20 646

92 905

8

53

72 279

79 382

20 618

92 897

7

54

72 299

79 410

20 590

92 889

6

55

72 320

79 438

20 562

92 881

5

56

72 340

79 466

20 534

92 874

4

57

72 360

79 495

20 505

92 866

3

58

72 381

79 523

20 477

92 858

2

59

72 401

79 551

20 449

92 850

1

60

72 421

79 579

20421

92 842

9

log COS

9

log cot

10

log tan

9

log sin

t

f

82°

43

r

log sin

log tan

log cot

log COS

f

9

72 421

9

79 579

10

20 421

9

92 842

60

1

72 441

79 607

20 393

92 834

59

2

72 461

79 635

20 365

92 826

58

3

72 482

79 663

20 337

92 818

57

4

72 502

79 691

20 309

92 810

56

5

72 522

79 719

20 281

92 803

55

6

72 542

79 747

20253

92 795

54

7

72 562

79 776

20 224

92 787

53

8

72 582

79 804

20196

92 779

52

9

72 602

79 832

20168

92 771^

51

10

72 622

79 860

20140

92 763'

50

11

72 643

79 888

20112

92 755

49

12

72 663

79 916

20 084

92 747

48

13

72 683

79 944

20 056

92 739

47

14

72 703

79 972

20 028

92 731

46

15

72 723

80 000

20 000

92 723

45

16

72 743

80028

19 972

92 715

44

17

72 763

80 056

19 944

92 707

43

18

72 783

80 084

19 916

92 699

42

19

72 803

80112

19 888

92 691

41

20

72 823

80140

19 860

92 683

40

21

72 843

80168

19 832

92 675

39

22

72 863

80195

19 805

92 667

38

23

72 883

80 223

19 777

92 659

37

24

72 902

80 251

19 749

92 651

36

25

72 922

80 279

19 721

92 643

35

26

72 942

80 307

19 693

92 635

34

27

72 962

80 335

19 665

92 627

33

28

72 982

80 363

19 637

92 619

32

29

73 002

80 391

19 609

92 611

31

30

73 022

80419

19 581

92 603

30

31

73 041

80 447

19 553

92 595

29

32

73 061

80 474

19 526

92 587

28

33

73 081

80 502

19 498

92 579

27

34

73 101

80 530

19 470

92 571

26

35

73 121

80 558

19 442

92 563

25

36

73 140

8b 586

19 414

92 555

24

37

73160

80 614

19 386

92 546

23

38

73180

80 642

19 358

92 538

22

39

73 200

80 669

19 331

92 530

21

40

73 219

80 697

19 303

92 522

20

41

73 239

80 725

19 275

92 514

19

42

73 259

80 753

19 247

92 506

18

43

73 278

80 781

19 219

92 498

17

44

73 298

80 808

19192

92 490

16

45

73 318

80 836

19164

92 482

15

46

73 337

80 864

19136

92 473

14

47

73 357

80 892

19108

^92 465

13

48

73 377

80919

19 081

92 457

12

49

73 396

80947

19 053

92 449

11

50

73 416

80 975

19 025

92 441

10

51

73 435

81003

18 997

92 433

9

52

73 455

81030

18 970

92 425

8

S3

73 474

81058

18 942

92 416

7

54

73 494

81086

18 914

92 408

6

55

73 513

81113

18 887

92 400

5

56

73 533

81141

18 859

92 392

4

57

73 552

81169

18 831

92 384

3

58

73 572

81196

18 804

92 376

2

59

73 591

81224

18 776

92 367

1

60

73 611

81252

18 748

92 359

9

log 008

9

log oot

10

log tan

9

log sin

t

t

68=

67'

44

83°

t

log sin

log tan

log oot

log 008

f

9

73 611

9

81252

10

18 748

9

92 359

60

1

73 630

81279

18 721

92 351

59

2

73 650

SI 307

18 693

92 343

58

3

73 669

81335

18 665

92 335

57

4

73 6S9

81362

18 638

92 326

56

6

73 70S

81390

18 610

92 318

65

6

73 727

81418

18 582

92 310

54

7

73 747

81445

18 555

92 302

53

8

73 766

81473

18 527

92 293

52

9

73 785

81500

ISiOO

92 285

51

10

73 805

81528

18 472

92 277

50

11

73 824

81 556

18 444

92 269

49

12

73 843

81583

18 417

92 260

48

13

73 863

81 611

18 389

92 252

47

14

73 882

SI 638

18 362

92 244

46

16

73 901

81666

18 334

92 235

46

16

73 921

81693

18 307

92 227

44

17

73 940

81721

18 279

92 219

43

18

73 959

81748

18 252

92 211

42

19

73 978

81776

18 224

92 202

41

20

73 997

81803

18197

92 194

40

21

74 017

81 831

18169

92186

39

22

74 036

81 858

18142

92 177

38

23

74 055

81SS6

18114

92 169

37

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74 074

81913

18 087

92161

36

25

74 093

819+1

18 059

92 152

36

26

74113

81 968

18 032

92144

34

27

74132

81996

IS 004

92 136

33

28

74151

82 023

17 977

92 127

32

29

74170

82 051

17 949

92 119

31

30

74189

82 078

17 922

92111

30

31

74 208

82106

17 89+

92 102

29

32

74 227

82 133

17 867

92 094

28

33

74 246

82 161

17 839

92 086

27

34

74 265

82188

17 812

92 077

26

36

74 284

82 215

17 785

92 069

25

36

74 303

82 243

17 757

92 060

24

37

74 322

82 270

17 730

92 052

23

38

74 341

82 298

17 702

92 0+4

22

39

74 360

82 325

17 675

92 035

21

40

74 379

82 352

17 648

92 027

20

41

74 398

82 380

17 620

92 018

19

42

74 417

82 407

17 593

92 010

18

43

74 436

82 435

17 565

92 002

17

44

74 455

82 462

17 538

91993

16

46

74 474

82 489

17 511

91985

16

46

74 493

82 517

17 483

91976

14

47

74 512

82 544

17 456

91968

13

48

74 531

82 571

17 429

91959

12

49

74 549

82 599

17 401

91951

11

50

74 568

82 626

17 374

91942

10

51

74 587

82 653

17 347

91934

9

52

74 606

82 681

17 319

91925

8

53

74 625

82 708

17 292

91917

7

54

74 644

82 735

17 265

91908

6

56

74 662

82 762

17 238

91900

5

56

74 681

82 790

17 210

91891

4

57

74 700

82 817

17 183

91883

3

58

74 719

82 844

17156

91874

2

59

74 737

82 871

17 129

91866

1

60

74 756

82 899

17101

91857

9

9

lO

9

/

logOOB

log cot

log tan

log sin

t

34'

t

log sin

log tan

log oot

leg 008

/

9

9

82 899

10

17101

9

91857

74 756

60

1

74 775

82 926

17 074

91S49

59

2

74 794

82 953

17 047

91840

58

3

74 812

82 980

17 020

91 832

57

4

74 831

83 008

16 992

91823

56

5

74 850

83 035

16 965

91815

56

6

74 868

83 062

16 938

91806

54

7

74 887

S3 089

16 911

91798

53

8

74 906

83 117

16 883

91789

52

9

74 924

83 144

16 856

91781

51

10

74 943

83 171

16 829

91772

60

11

74 961

83 198

16 802

91763

49

12

74 980

83 225

16 775

91755

48

13

74 999

83 252

16 748

91746

47

14

75 017

83 280

16 720

91738

46

15

75 036

83 307

16 693

91729

46

16

75 054

83 334

16 666

91720

44

17

75 073

83 361

16 639

91712

43

18

75 091

83 3SS

16 612

91703

42

19

75 110

83 415

16 585-

91695

41

20

75 128

83 442

16 558

91686

40

21

75 147

S3 470

16 530

91677

39

22

75 165

S3 497

16 503

91669

38

23

75 184

S3 524

16 476

91660

37

24

75 202

S3 551

16 449

91651

36

25

75 221

S3 578

16 422

91643

36

26

75 239

83 605

16 395

91634

34

27

75 258

83 632

16 368

91625

33

28

75 276

83 659

16 341

91617

32

29

75 294

S3 686

16 314

91608

31

30

75 313

83 713

16 287

91599

30

31

75 331

83 740

16 260

91591

29

32

75 350

S3 768

16 232

91582

28

33

75 368

83 795

16 205

91573

27

34

75 386

83 822

16178

91565

26

36

75 405

83 849

16151

91556

25

36

75 423

83 876

16124

91547

24

37

75 441

83 903

16 097

91538

23

38

75 459

83 930

16 070

91530

22

39

75 478

83 957

16 043

91521

21

40

75 496

83 984

16 016

91512

20

41

75 514

84 011

15 989

91504

19

42

75 533

84 038

15 962

91495

18

43

75 551

84 065

15 935

91 486

17

44

75 569

84 092

15 908

91477

16

46

75 587

84 119

15 881

91469

15

46

75 605

84146

15 854

91460

14

47

75 624

84 173

15 827

91451

13

48

75 642

84 200

15 800

91442

12

49

75 660

84 227

15 773

91433

11

50

75 678

84 254

15 746

91425

lO

51

75 696

84 280

15 720

91416

9

52

75 714

84 307

15 693

91407

8

53

75 733

84 334

15 666

91398

7

54

75 751

84 361

15 639

91389

6

65

75 769

84 388

15 612

91 381

5

56

75 787

84 415

15 585

91372

4

57

75 805

84 442

15 558

91363

3

58

75 823

84 469

15 531

91354

2

59

75 841

84 496

15 504

91345

1

60

75 859

84 523

15 477

91336

O

9

log 008

9

log oot

10

log tan

9

log sin

t

t

56'

56'

36°

t

log sin

log tan

log cot

log 008

f

9

75 859

9

84 523

10

15 477

9

91336

o

60

1

75 877

84 550

15 450

91328

59

2

75 895

84 576

15 424

91319

58

3

75 913

84 603

15 397

91310

57

. 4

75 931

84 630

15 370

91301

56

5

75 949

84 657

15 343

91292

55

6

75 967

84 684

15 316

91283

54

7

75 985

84 711

15 289

91274

53

8

76 003

84 738

15 262

91266

52

9

76 021

84 764

15 236

91257

51

lO

76 039

84 791

15 209

91248

50

11

76 057

84 818

15 182

91239

49

12

76 075

84 845

15 155

91230

48

13

76 093

84 872

15 128

91 221

47

14

76111

84 899

15 101

91212

46

15

76129

84 925

15 075

91203

45

16

76146

84 952

15 048

91194

44

17

76164

84 979

15 021

91 185

43

18

76182

85 006

14 994

91176

42

19

76 200

85 033

14 967

91167

41

20

76 218

85 059

14 941

91158

40

21

76 236

85 086

14 914

91149

39

22

76 253

85 113

14 887

91141

38

23

76 271

85 140

14 860

91132

37

24

76 289

85 166

14 834

91123

36

25

76 307

85 193

14 807

91114

35

26

76 324

85 220

14 780

91105

34

27

76 342

85 247

14 753

91096

33

28

76 360

85 273

14 727

91087

32

29

76 378

85 300

14 700

91078

31

30

76 395

85 327

14 673

91069

30

31

76 413

85 354

14 646

91060

29

32

76 431

85 380

14 620

91051

28

33

76 448

85 407

14 593

91042

27

34

76 466

85 434

14 566

91033

26

35

76484

85 460

14 540

91023

25

36

76 501

85 487

14 513

91014

24

37

76 519

85 514

14 486

91005

23

38

76 537

85 540

14 460

90 996

22

39

76 554

85 567

14 433

90 987

21

40

76 572

85 594

14 406

90 978

20

41

76 590

85 620

14 380

90 969

19

42

76 607

85 647

14 353

90 960

18

43

76 625

85 674

14 326

90 951

17

44

76 642

85 700

14 300

90 942

16

45

76 660

85 727

14 273

90 933

15

46

76 677

85 754

14 246

90 924

14

47

76 695

85 780

14 220

90 915

13

48

76 712

85 807

14193

90 906

12

49

76 730

85 834

14166

90 896

11

50

76 747

85 860

14 140

90 887

10

51

76 765

85 887

14 113

90 878

9

52

76 782

85 913

14 087

90 869

8

53

76 800

85 940

14 060

90 860

7

54

76 817

85 967

14 033

90 851

6

55

76 835

85 993

14 007

90 842

5

56

76 852

86 020

13 980

90 832

4

57

76 870

86 046

13 954

90 823

3

58

76 887

86 073

13 927

90 814

2

59

76 904

86100

13 900

90 805

1

60

76 922

86126

13 874

90 796

9

log cos

9

log cot

lO

log tan

9

log sin

t

t

36°

46

t

log sin

log tan

log cot

log 008

f

9

76 922

9

86126

10

13 874

9

90 796

o

60

1

76 939

86153

13 847

90 787

59

2

76 957

86 179

13 821

90 777

58

3

76 974

86 206

13 794

90 768

57

4

76 991

86 232

13 768

90 759

56

5

77 009

86 259

13 741

90 750

55

6

77 026

86 285

13 715

90 741

54

7

77 043

86 312

13 688

90 731

53

8

77 061

86 338

13 662

90 722

52

9

77 078

86 365

13 635

90 713

51

10

77 095

86 392

13 608

90 704

50

11

77 112

86 418

13 582

90 694

49

12

77 130

86 445

13 555

90 685

48

13

77147

86 471

13 529

90 676

47

14

77164

86 498

13 502

90 667

46

15

77 181

86 524

13 476

90 657

45

16

77 199

86 551

13 449

90 648

44

17

77 216

86 577

13 423

90 639

43

18

77 233

86 603

13 397

90 630

42

19

77 250

86 630

13 370

90 620

41

20

77 268

86 656

13 344

90 611

40

21

77 285

86 683

13 317

90 602

39

22

77 302

86 709

13 291

90 592

38

23

77 319

86 736

13 264

90 583

37

24

77 336

86 762

13 238

90 574

36

25

77 353

86 789

13 211

90 565

35

26

77 370

86 815

13 185

90 555

34

27

77 387

86 842

13 158

90 546

33

28

77 405

86 868

13 132

90 537

32

29

77 422

86 894

13 106

90 527

31

30

77 439

86 921

13 079

90 518

30

31

77 456

86 947

13 053

90 509

29

32

77 473

86 974

13 026

90 499

28

33

77 490

87 000

13 000

90 490

27

34

77 507

87 027

12 973

90 480

26

35

77 524

87 053

12 947

90 471

25

36

77 541

87 079

12 921

90 462

24

37

77 558-

87 106

12 894

90 452

23

38

77 575

87 132

12 868

90 443

22

39

77 592

87158

12 842

90 434

21

40

77 609

87185

12 815

90 424

20

41

77 626

87 211

12 789

90 415

19

42

77 643

87 238

12 762

90 405

18

43

77 660

87 264

12 736

90 396

17

44

77 677

87 290

12 710

90 386

16

45

77 694

87 317

12 683

90 377

15

46

77 711

87 343

12 657

90 368

14

47

77 728

87 369

12 631

90 358

13

48

77 744

87 396

12 604

90 349

12

49

77 761

87 422

12 578

90 339

11

50

77 778

87 448

12 552

90 330

10

51

77 795

87 475

12 525

90 320

9

52

77 812

87 501

12 499

90 311

8

53

77 829

87 527

12 473

90 301

7

54

77 846

87 554

12 446

90 292

6

55

77 862

87 580

12 420

90 282

5

56

77 879

87 606

12 394

90 273

4

57

77 896

87 633

12 367

90 263

3

58

77 913

87 659

12 341

90 254

2

59

77 930

87 685

12315

90 244

1

60

77 946

87 711

12 289

90 235

9

log oos

9

log cot

lO

log tan

9

log sin

/

t

54^

53'

46

3r

t

log sin

log tan

log oot

log COS

t

9

77 946

9

87 711

lO

12 289

9

90 235

O

60

1

77 963

87 738

12 262

90 225

59

2

77 980

87 764

12 236

90 216

58

3

77 997

87 790

12 210

90 206

57

4

78 013

87 817

12183

90197

56

5

78 030

87 843

12 157

90187

55

6

78 (H7

87 869

12 131

90178

54

7

78 063

87 895

12105

90168

53

8

78 080

87 922

12 078

90159

52

. 9

78 097

87 948

12 052

90149

51

lO

78113

87 974

12 026

90139

50

11

78130

88 000

12 000

90130

49

12

78147

88 027

11973

90120

48

13

78163

88 053

11947

90111

47

14

78180

88 079

11921

90101

46

15

78197

88 105

11895

90 091

45

16

78 213

88131

11869

90 082

44

17

78 230

88158

11842

90 072

43

IS

78 246

88184

11816

90 063

42

19

78 263

88 210

11790

90 053

41

20

78 280

88 236

11764

90 043

40

21

78 296

88 262

11738

90 034

39

22

78 313

88 289

11711

90 024

38

23

78 329

88 315

11 685

90 014

37

24

78 346

88 341

11659

90 005

36

25

78 362

88 367

11633

89 995

35

26

78 379

88 393

11607

89 985

34

27

78 395

88 420

11580

89 976

32,

28

78 412

88 446

11554

89 966

32

29

78 428

88 472

11528

89 956

31

30

78 445

88 498

11502

89 947

30

31

78 461

88 524

11476

89 937

29

32

78 478

88 550

11450

89 927

28

33

78 494

88 577

11423

89 918

27

34

78 510

88 603

11397

89 908

26

35

78 527

88 629

11371

89 898

25

36

78 543

88 655

11345

89 888

24

37

78 560

88 681

11319

89 879

23

38

78 576

88 707

11293

89 869

22

39

78 592

88 733

11267

89 859

21

40

78 609

88 759

11241

89 849

20

41

78 625

88 786

11214

89 840

19

42

78 642

88 812

11188

89 830

18

43

78658

88 838

11162

89 820

17

44

78 674

88 864

11136

89 810

16

45

78 691

88 890

11110

89 801

15

46

78 707

88 916

11084

89 791

14

47

78 723

88 942

11058

89 781

13

48

78 739

88 968

11032

89 771

12

49

78 756

88 994

11006

89 761

11

50

78 772

89 020

10 980

89 752

10

51

78 788

89 046

10 954

89 742

9

52

78 805

89 073

10927

89 732

8

S3

78 821

89 099

10 901

89 722

7

54

78 837

8912i

10 875

89 712

6

55

78 853

89151

10 849

89 702

5

56

78 869

89177

10 823

89 693

4

57

78 886

89 203

10 797

89 683

3

58

78 902

89 229

10 771

89 673

2

59

78 918

89 255

10 745

89 663

1

60

78934

89 281

10 719

89 653

O

9

log 008

9

log oot

lO

log tan

9

log sin

t

t

38=

1

log sin

log tan

log oot

log COB

/

9

78 934

9

89 281

10

10 719

9

89 653

60

1

78 950

89 307

10 693

89 643

59

2

78 967

89 333

10 667

89 633

58

3

78 983

89 359

10 641

89 624

57

4

78 999

89 385

10 615

89 614

56

5

79 015

89 411

10 589

89 604

55

6

79 031

89 437

10 563

89 594

54

7

79 047

89 463

10 537

89 584

53

8

79 063

89 489

10 511

89 574

52

9

19^19

89 515

10 485

89 564

51

10

79 095

89 541

10 459

89 554

50

11

79111

89 567

10 433

89 544

49

12

79128

89 593

10 407

89 534

48

13

79144

89 619

10 381

89 524

47

14

79160

89 645

10 355

89 514

46

15

79176

89 671

10 329

89 504

45

16

79192

89 697

10 303

89 495

44

17

79 208

89 723

10 277

89 485

43

18

79 224

89 749

10 251

89 475

42

19

79 240

89 775

10 225

89 465

41

20

79 256

89 801

10199

89 455

40

21

79 272

89 827

10173

89 445

39

22

79 288

89 853

10 147

89 435

38

23

79 304

89 879

10121

89 425

37

24

79 319

89 905

10 095

89 415

36

25

79 335

89 931

10 069

89405

35

26

79 351

89 957

10 043

89 395

34

27

79 367

89 983

10 017

89 385

33

28

79 383

90 009

09 991

89 375

32

29

79 399

90 035

09 965

89 364

31

30

79 415

90 061

09 939

89 354

30

31

79 431

90 086

09 914

89 344

29

32

79 447

90 112

09 888

89 334

28

33

79 463

90138

09 862

89 324

27

34

79 478

90164

09 836

89 314

26

35

79 494

90190

09 810

89 304

25

36

79 510

90 216

09 784

89 294

24

37

79 526

90 242

09 758

89 284

23

38

79 542

90 268

09 732

89 274

22

39

79 558

90 294

09 706

89 264

21

40

79 573

90 320

09 680

89 254

20

41

79 589

90 346

09 654

89 244

19

42

79 605

90 371

09 629

89 233

18

43

79 621

90 397

09 603

89 223

17

44

79 636

90 423

09 577

89 213

16

45

79 652

90 449

09 551

89 203

15

46

79 668

90 475

09 525

89193

14

47

79 684

90 501

09 499

89183

13

48

79 699

90 527

09 473

89173

12

49

79 715

90 553

09 447

89162

11

50

79 731

90 578

09 422

89152

lO

51

79 746

90 604

09 396

89 142

9

52

79 762

90 630

09 370.

89132

8

53

79 778

90 656

09 344

89122

7

54

79 793

90 682

09 318

89112

6

55

79 809

90 708

09 292

89101

5

56

79 825

90 734

09 266

89 091

4

57

79 840

90 759

09 241

89 081

3

58

79 856

90 785

09 215

89 071

2

59

79 872

90 811

09189

89 060

1

60

79 887

90 837

09163

89 050

O

9

9

10

9

f

log 008

log oot

log tan

log8in

9

52'

hX

39'

r

log sin

log tan

log cot

log 008

f

9

79 887

9

90 837

10

09163

9

89 050

O

60

1

79 903

90 863

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89 040

59

2

79 918

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58

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79 934

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57

4

79 950

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56

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79 965

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88 999

55

6

79 981

90 992

09 008

88 989

54

7

79 996

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08 982

88 978

53

8

80 012

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08 957

88 968

52

9

80 027

91069

08 931

88 958

51

lO

80 043

91095

08 905

88 948

50

11

80 058

91121

08 879

88 937

49

12

80 074

91147

08 853

88 927

48

13

80 089

91172

08 828

88 917

47

14

80105

91198

08 802

88 906

46

15

80120

91224

08 776

88 896

45

16

80136

91250

08 750

88 886

44

17

80151

91276

08 724

88 875

43

18

80166

91301

08 699

88 865

42

19

80182

91327

08 673

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41

20

80197

91353

08 647

88 844

40

21

80 213

91379

08 621

88 834

39

22

80 228

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08 596

88 824

38

23

80 244

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88 813

37

24

80 259

91456

08 544

88 803

36

25

80 274

91482

08 518

88 793

35

26

80 290

91507

08 493

88 782

34

27

80 305

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08 467

88 772

33

28

80 320

91559

08 441

88 761

32

29

80 336

91585

08 415

88 751

31

30

80351

91610

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88 741

30

31

80 366

91636

08 364

88 730

29

32

80 382

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88 720

28

33

80 397

91688

08 312

88 709

27

34

80 412

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88 699

26

35

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88 688

25

36

80 443

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88 678

24

37

80 458

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88 668

23

38

80 473

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88 657

22

39

80 489

91842

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21

40

80 504

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20

41

80 519

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88 626

19

42

80 534

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08 081

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18

43

80 550

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08 055

88 605

17

44

80 565

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08 029

88 594

16

45

80 580

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08 004

88 584

15

46

80 595

92 022

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88 573

14

47

80 610

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13

48

80 625

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12

49

80 641

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11

50

80 656

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lO

51

80 671

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88 521 ■

9

52

80 686

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8

53

80 701

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7

54

80 716

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6

55

80 731

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07 747

88 478

5

56

80 746

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07 721

88 468

4

57

80 762

92 304

07 696

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3

58

80 777

92 330

07 670

88 447

2

59

80 792

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07 644

88 436

1

60

80 807

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07 619

88 425

9

9

lO

9

f

log oos

log cot

log tan

log sin

f

40°

47

t

log sin

log tan

log cot

log cos

f

-.

9

9

lO

9

80 807

92 381

07 619

88 425

60

1

80 822

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59

2

80 837

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58

3

80 852

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57

4

80 867

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56

5

80 882

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55

6

80 897

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54

7

80 912

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53
52

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9

80 942

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51

10

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50

11

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49

12

80 987

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48

13

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47

14

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46

15

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45

16

81047

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44

17

81061

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43

18

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42

19

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41

20

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40

21

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39

22

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38

23

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37

24

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36

25

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35

26

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27

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33

28

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32

29

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31

30

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30

31

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29

32

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28

33

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27

34

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06 748

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26

35

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36

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24

37

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23

38

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06 646

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22

39

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40

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20

41

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42

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43

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44

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16

45

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14

47

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13

48

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12

49

81534

93 636

06 364

87 898

11

50

81549

93 661

06 339

87 887

10

51

81563

93 687

06 313

87 877

9

52

81578

93 712

06 288

87 866

8

53

81592

93 738

06 262

87 855

7

54

81607

93 763

06 237

87 844

6

55

81622

93 789

06 211

87 833

5

56

81636

93 814

06186

87 822

4

57

81651

93 840

06 160

87 811

3

58

81665

93 865

06135

87 800

2

59

81680

93 891

06109

87 789

1

60

81694

93 916

06 084

87 778

9

9

lO

9

f

log oos

log cot

log tan

log sin

t

m

49'

48

4'

V

t

log sin

log tan

log cot

log cos

t

9

9

10

9

O

81694

93 916

06 084

87 778

60

1

81709

93 942

06 058

87 767

59

2

81723

93 967

06 033

87 756

58

3

81738

93 993

06 007

87 745

57

4

81 752

94 018

05 982

87 734

56

5

81767

94 044

05 956

87 723

55

6

81781

94 069

05 931

87 712

54

7

81796

94 095

05 905

87 701

53

8

81810

94 120

05 880

87 690

52

9

8182i

94 146

05 854

87 679

51

10

81839

94 171

05 829

87 668

50

11

81854

94 197

05 803

87 657

49

12

81868

94 222

05 778

87 646

48

13

81882

94 248

05 752

87 635

47

14

81897

94 273

05 727

87 624

46

15

81911

94 299

05 701

87 613

45

16

81926

94 324

05 676

87 601

44

17

81940

94 350

05 650

87 590

43

18

81 955

94 375

05 625

87 579

42

19

81969

94 401

05 599

87 568

41

20

81983

94 426

05 574

87 557

40

21

81998

94 452

05 548

87 546

39

22

82 012

94 477

05 523

87 535

38

23

82 026

94 503

05 497

87 524

37

24

82 041

94 528

05 472

87 513

36

25

82 055

94 554

05 446

87 501

35

26

82 069

94 579

05 421

87 490

34

27

82 084

94 604

05 396

87 479

33

28

82 098

94 630

05 370

87 468

32

29

82 112

94 655

05 345

87 457

31

30

82 126

94 681

05 319

87 446

30

31

82 141

94 706

05 294

87 434

29

32

82 155

94 732

05 268

87 423

28

ZZ

82 169

94 757

05 243

87 412

27

34

82 184

94783

05 217

87 401

26

35

82 198

94 808

05 192

87 390

25

36

82 212

94 834

05 166

87 378

24

37

82 226

94 859

05 141

87 367

23

38

82 240

94 884

05 116

87 356

22

39

82 25i

94 910

05 090

87 345

21

40

82 269

94 935

05 065

87 334

20

41

82 283

94 961

05 039

87 322

19

42

82 297

94 986

05 014

87 311

18

43

82 311

95 012

04 988

87 300

17

44

82 326

95 037

04 963

87 288

16

45

82 340

95 062

04 938

87 277

15

46

82 354

95 088

04 912

87 266

14

47

82 368

95 113

04 887

87 255

13

48

82 382

95 139

04 861

87 243

12

49

82 396

95 164

04 836

87 232

11

50

82 410

95 190

04 810

87 221

10

51

82 424

95 215

04 785

87 209

9

52

82 439

95 240

04 760

87198

8

53

82 453

95 266

04 734

87 187

7

54

82 467

95 291

04 709

87 175

6

56

82 481

95 317

04 683

87 164

5

56

82 495

95 342

04 658

87 153

4

57

82 509

95 368

04 632

87 141

3

58

82 523

95 393

04 607

87 130

2

59

82 537

95 418

04 582

87 119

1

60

82 551

95 444

04 556

87 107

9

log cos

9

log cot

lO

log tan

9

log sin

t

t

42°

t

log sin

log tan

log cot

log cos

/

9

9

lO

9

o

82 551

95 444

04 556

87 107

60

1

82 565

95 469

04 531

87 096

59

2

82 579

95 495

04 505

87 085

58

3

82 593

95 520

04 480

87 073

57

4

82 607

95 545

04 455

87 062

56

5

82 621

95 571

04 429

87 050

55

6

82 635

95 596

04 404

87 039

54

7

82 649

95 622

04 378

87 028

53

8

82 663

95 647

04 353

87 016

52

9

82 677

95 672

04 328

87 005

51

10

82 691

95 698

04 302

86 993

50

11

82 705

95 723

04 277

86 982

49

12

82 719

95 748

04 252

86 970

48

13

82 733

95 774

04 226

86 959

47

14

82 747

95 799

04 201

86 947

46

15

82 761

95 825

04 175

86 936

45

16

82 775

95 850

04 150

86 924

44

17

82 788

95 875

04 125

86 913

43

18

82 802

95 901

04 099

86 902

42

19

82 816

95 926

04 074

86 890

41

20

82 830

95 952

04 048

86 879

40

21

82 844

95 977

04 023

86 867

39

22

82 858

96 002

03 998

86 855

38

23

82 872

96 028

03 972

86 844

37

24

82 885

96 053

03 947

86 832

36

25

82 899

96 078

03 922

86 821

35

26

82 913

96104

03 896

86 809

34

27

82 927

96129

03 871

86 798

33

28

82 941

96155

03 845

86 786

32

29

82 955

96180

03 820

86 775

31

30

82 968

96 205

03 795

86 763

30

31

82 982

96 231

03 769

86 752

29

32

82 996

96 256

03 744

86 740

28

ZZ

83 010

96 281

03 719

86 728

27

34

83 023

96 307

03 693

86 717

26

35

83 037

96 332

03 668

86 705

25

36

83 051

96 357

03 643

86 694

24

37

83 065

96 383

03 617

86 682

23

38

83 078

96 408

03 592

86 670

22

39

83 092

96 433

03 567

86 659

21

40

83 106

96 459

03 541

86 647

20

41

83 120

96 484

03 516

86 635

19

42

83 133

96 510

03 490

86 624

18

43

83 147

96 535

03 465

86 612

17

44

83 161

96 560

03 440

86 600

16

45

83 174

96 586

03 414

86 589

15

46

83 188

96 611

03 389

86 577

14

47

83 202

96 636

03 364

86 565

13

48

83 215

96 662

03 338

86 554

12

49

83 229

96 687

03 313

86 542

11

50

83 242

96 712

03 288

86 530

lO

51

83 256

96 738

03 262

86 518

9

52

83 270

96 763

03 237

86 507

8

53

83 283

96 788

03 212

86 495

7

54

83 297

96 814

03 186

86 483

6

55

83 310

96 839

03 161

86 472

5

56

83 324

96 864

03 136

86 460

4

57

83 338

96 890

03 110

86 448

3

58

83 351

96 915

03 085

86 436

2

59

83 365

96 940

03 060

86 425

1

60

83 378

%966

03 034

86413

O

9

9

lO

9

t

log cos

log cot

log tan

log sin

f

48'

470

43^

r

log sin

log tan

log cot

log 008

r

9

83 378

9

96 966

lO

03 034

9

86 413

O

60

1

83 392

96 991

03 009

86 401

59

2

83 405

97 016

02 984

86 389

58

3

83 419

97 042

02 958

86 377

57

4

83 432

97 067

02 933

86 366

56

5

83 446

97 092

02 908

86 354

55

6

83 459

97118

02 882

86 342

54

7

83 473

97 143

02 857

86 330

53

8

83 486

97 168

02 832

86 318

52

9

83 500

97 193

02 807

86 306

51

lO

83 513

97 219

02 781

86 295

50

11

83 527

97 244

02 756

86 283

49

12

83 540

97 269

02 731

86 271

48

13

83 554

97 295

02 705

86 259

47

14

83 567

97 320

02 680

86 247

46

15

83 581

97 345

02 655

86 235

45

16

83 594

97 371

02 629

86 223

44

17

83 608

97 396

02 604

86 211

43

18

83 621

97 421

02 579

86 200

42

19

83 634

97 447

02 553

86188

41

20

83 648

97 472

02 528

86 176

40

21

83 661

97 497

02 503

86164

39

22

83 674

97 523

02 477

86 152

38

23

83 688

97 548

02 452

86140

37

24

83 701

97 573

02 427

86128

36

25

83 715

97 598

02 402

86116

35

26

83 728

97 624

02 376

86104

34

27

83 741

97 649

02 351

86 092

33

28

83 755

97 674

02 326

86 080

31

29

83 768

97 700

02 300

86 068

31

30

83 781

97 725

02 275

86 056

30

31

83 795

97 750

02 250

86 044

29

32

83 808

97 776

02 224

86 032

28

33

83 821

97 801

02199

86 020

27

34

83 834

97 826

02 174

86 008

26

35

83 848

97 851

02 149

85 996

25

36

83 861

97 877

02 123

85 984

24

37

83 874

97 902

02 098

85 972

23

38

83 887

97 927

02 073

85 960

22

39

83 901

97 953

02 047

85 948

21

40

83 914

97 978

02 022

85 936

20

41

83 927

98 003

01997

85 924

19

42

83 940

98 029

01971

85 912

18

43

83 954

98 054

01946

85 900

17

44

83 967

98 079

01921

85 888

16

45

83 980

98104

01896

85 876

15

46

83 993

98130

01870

85 864

14

47

84 006

98 155

01845

85 851

13

48

84 020

98180

01820

85 839

12

49

84 033

98 206

01794

85 827

11

50

84 046

98 231

01769

85 815

10

51

84 059

98 256

01744

85 803

9

52

84 072

98 281

01719

85 791

8

53

84 085

98 307

01693

85 779

7

54

84 098

98 332

01668

85 766

6

55

84112

98 357

01643

85 754

5

56

84 125

98 383

01617

85 742

4

57

84 138

98 408

01592

85 730

3

58

84 151

98 433

01567

85 718

2

59

84 164

98 458

01542

85 706

1

60

84 177

98 484

01516

85 693

<»

9

log oos

9

log cot

10

log tan

9

log sin

f

440

49

f

log sin

log tan

log cot

log cos

/

9

84177

9

98 484

10

01516

9

85 693

60

1

84190

98 509

01491

85 681

59

2

84 203

98 534

01466

85 669

58

3

84 216

98 560

01440

85 657

57

4

84 229

98 585

01415

85 645

56

5

84 242

98 610

01390

85 632

55

6

84 255

98 635

01365

85 620

54

7

84 269

98 661

01339

85 608

53

8

84 282

98 686

01314

85 596

52

9

84 295

98 711

01289

85 583

51

10

84 308

98 737

01263

85 571

50

11

84 321.

98 762

01238

85 559

49

12

84 334

98 787

01213

85 547

48

13

84 347

98 812

01188

85 534

47

14

84 360

98 838

01162

85 522

46

15

84 373

98 863

01137

85 510

45

16

84 385

98 888

01112

85 497

44

17

84 398

98 913

01087

85 485

43

18

84 411

98 939

01061

85 475

42

19

84 424

98 964

01036

85 460

41

20

84 437

98 989

01011

85 448

40

21

84 450

99 015

00 985

85 436

39

22

84 463

99 040

00 960

85 423

38

23

84 476

99 065

00 935

85 411

37

24

84 489

99 090

00 910

85 399

36

25

84 502

99 116

00 884

85 386

35

26

84 515

99 141

00 859

85 374

34

27

84 528

99 166

00 834

85 361

33

28

84 540

99 191

00 809

85 349

32

29

84 553

99 217

00 783

85 337

31

30

84 566

99 242

00 758

85 324

30

31

84 579

99 267

00 733

85 312

29

32

84 592

99 293

00 707

85 299

28

33

84 605

99 318

00 682

85 287

27

34

84 618

99 343

00 657

85 274

26

35

84 630

99 368

00 632

85 262

25

36

84 643

99 394

00 606

85 250

24

37

84 656

99 419

00 581

85 237

23

38

84 669

99 444

00 556

85 225

22

39

84 682

99 469

00 531

85 212

21

40

84 694

99 495

00 505

85 200

20

41

84 707

99 520

00 480

85 187

19

42

84 720

99 545

00 455

85 17i

18

43

84 733

99 570

00 430

85 162

17

44

84 745

99 596

00 404

85 150

16

45

84 758

99 621

00 379

85 137

15

46

84 771

99 646

00 354

85 125

14

47

84 784

99 672

00 328

85 112

13

48

84 796

99 697

00 303

85 100

12

49

84 809

99 722

00 278

85 087

11

50

84 822

99 747

00 253

85 074

10

51

84 835

99 773

00 227

85 062

9

52

84 847

99 798

00 202

85 049

8

53

84 860

99 823

00 177

85 037

7

54

84 873

99 848

00 152

85 024

6

55

84 885

99 874

00126

85 012

5

56

84 898

99 899

00101

84 999

4

57

84 911

99 924

00 076

84 986

3

58

84 923

99 949

00 051

84 974

2

59

84 936

99 975

00 025

84 961

1

60

84 949

00 000

00 000

84 949

9

10

10

9

f

log cos

log cot

log tan

log sin

t

m

46'

50

TABLE IV.

HAN CAN BE DONE BY

Fob Determining with

Greater Accuracy t

MEANS OF Table III. :

1. log sin, log tan, and log cot, when the angle is between 0° and 2

o .

•>

2. log cos, log tan, and log cot, when the angle is between 88° and 90° ;

3. The value of the angle when the logarithm of the function does not

lie between the limits 8. 54 684 and 11. 45 316.

1

FORMULAS FOR THE USE OF THE NUMBERS S AND T.

I. When the angle a is between 0° and 2° :

log sin a = log a" + S.

log a" = log sin a — S,

log tan a = log a" + T.

= log tan a — T,

log cot a = colog tan o.

= colog cot a— T.

11. When the angle a is between 88° and 90° :

log cos a = log (90° - o)" + S.

log (90° - a)" = log cos a -

-s,

log cot a = log (90° - a)" + T.

= log cot o -

- T,

log tan a = colog cot a.

= colog tan a — T, 1

and a = 90° - (90^

'-«).

Values of S ai^t> T.

a" S log sin a

a" T log tan a

O T

log tan a

—

—

5146

8. 39 713

4. 68 557

4. 68 557

4. 68 567

2 409 8. 06 740

200 6. 98 660

5 424

8. 41 999

4. 68 556

4. 68 558

4. 68 568

3 417 . 8. 21 920

1 726 7. 92 263

5 689

8. 44 072

4. 68 555

4. 68 559

4. 68 569

3 823 8. 26 795

2 432 8. 07 156

5 941

8. 45 955

4. 68 555

4. 68 560

4. 68 570

4 190 8. 30 776

2 976 8. 15 924

6184

8. 47 697

4. 68 554

4. 68 561

4. 68 571

4 840 8. 37 038

3 434 8. 22 142

6 417

8.49 305

4.68 553

4. 68 562

4. 68 572

5 414 8. 41 904

3 838 8. 26 973

6 642

8. 50 802

4. 68 552

4. 68 563

4. 68 573

5 932 8. 45 872

4 204 8.30 930

6 859

8. 52 200

4.68 551

4. 68 564

4. 68 574

6 408 8.49 223

4 540 8. 34 270

7 070

8.53 516

4. 68 550

4. 68 565

4. 68 575

6 633 8.50 721

4 699 8. 35 766

7173

8. 54 145

4. 68 5iO

4. 68 565

4.68 575

6 851 8. 52 125

4 853 8. 37 167

7 274

8. 54 753

4. 68 549

4. 68 566

7 267 8. 54 684

5 146 8. 39 713

a" S log sin a

a" T log tan a

a T

log tan a

TABLE v.— Circumferences AND Areas OF Circles, si

\1 N= the radius of the circle, the circumference = 2ir

iV.

If iV = the radius of the circle, the area

«7rJV^.

[f iV = the circumference of the circle, the rad

ius = —
27r

N.

UN = the circumference of the circle, the area = —

4ir

K^.

N

iiTN

■KN*

2rr

N

27riV

TTjft

2ir

4-7r

1
2
3
4

0.00

6.28

12.57

18.85

25.13

0.0

3.1

12.6

28.3

50.3

0.000
0.155
0.318
0.477
0.637

0.00
0.08
0.32
0.72
1.27

50

51
52
53
54

314. 16
320. 44
326. 73
333. 01
339. 29

7 854
8171

8 495
8 825
9161

7.96
8.12
8.28
8.44
8.59

198. 94
206. 98
215. 18
223. 53
232. Oi

6

6

7
8
9

31.42
37.70
43.98
50.27
56.55

78.5
113.1
153.9
201.1
254.5

0.796
0.955
1.114
1.273
1.432

1.99
2.86
3.90
5.09
6.45

55

56
57
58
59

345. 58
351.86
358. 14
364. 42
370. 7i

9 503

9 852

10 207

10 568

10 936

8.75
8.91
9.07
9.23
9.39

240. 72
249. 55
258. 5i
267. 70
277.01

10

11
12
13
14

62.83
69.12
75.40
81.68
87.96

314.2
380.1
452.4
530.9
615.8

1.592
1.751
1.910
2.069

2.228

7.96

9.63

11.46

13.45

15.60

60

61
62
63

64

376. 99
383. 27
389. 56
395. 84
402. 12

11310
11690
12 076
12 469
12 868

9.55

9.71

9.87

10.03

10.19

286. 48
296. 11
305. 90
315. 84
325. 9i

15

16
17
18
19

94.25
100. 53
106. 81
113. 10
119. 38

706.9

804.2

907.9

1017.9

1 134. 1

2.387
2.546
2.706
2.865
3.024

17.90
20.37
23.00

25.78
28.73

65

66
67
68
69

408. 41
414. 69
420. 97
427. 26
433. 54

13 273

13 685
14103

14 527
14 957

10.35
10.50
10.66
10.82
10.98

336. 21
346. 64
357. 22
367. 97
378. 87

20

21
22
23
24

125. 66
131.95
138. 23
144. 51
150. 80

1 256. 6
1 385. 4
1 520. 5
1 661. 9
1 809. 6

3.183
3.342
3.501
3.661
3.820

31.83
35. 09
38.52
42.10
45.84

70

71
72
73
74

439. 82
446. 11
452. 39
458. 67
464.96

15 394

15 837

16 286

16 742

17 203

11.14
11.30
11.46
11.62
11.78

389. 93
401. 15
412. 53
424. 07
435. 77

25

26

27
28
29

157. 08
163. 36
169. 65
175. 93
182. 21

1 963. 5

2 123. 7
2 290. 2
2 463.
2 642. 1

3.979
4.138
4.297
4.456
4.615

49.74
53.79
58.01
62.39
66.92

75

76
77
78
79

471. 24
477. 52
483, 81
490.09
496. 37

17 671

18 146

18 627
19113

19 607

11.94
12.10
12.25
12.41
12.57

447. 62
459. 64
471.81
484. 15
496. 64

30

31
32
33
34

188. 50
194. 78
201. 06
207. 35
213. 63

2 827. 4

3 019. 1
3 217.0
3 421.2
3 631.7

4.775
4.934
5.093
5.252
5.411

71.62
76.47
81.49
86.66
91.99

80

81
82
83
84

502. 65
508. 94
515.22
521. 50
527. 79

20106
20 612
21124
21642
22 167

12.73
12.89
13.05
13.21
13.37

509. 30
522. 11
535. 08
548. 21
561. 50

35

36
37
38
39

219. 91
226. 19
232. 48
238. 76
245. 04

3 848. 5

4 071.5
4 300. 8
4 536. 5
4 778. 4

5.570
5.730
5.889
6.048
6.207

97.48
103. 13
108. 94
114. 91
121. 04

85

86
87
88
89

534. 07
540. 35
546. 64
552. 92
559. 20

22^8
23 235

23 779

24 328
24 885

13.53
13.69
13.85
14.01
14.16

574. 95
588. 55
602. 32
616. 25
630. 33

40

41
42
43

44

251. 33
257. 61
263.89
270. 18
276. 46

5 026. 5
5 281.0
5 541.8

5 80S. 8

6 082. 1

6.366
6.525
6 685
6.844
7.003

127. 32
133. 77
140. 37
147. 14
154. 06

90

91
92
93
94

565. 49
571.77
578. 05
584. 34
590.62

25 447

26 016

26 590

27 172
27 759

14. 32
14.48
14.64
14.80
14.96

644. 58
658. 98
673. 54
688. 27
703. 15

45

46
47
48
49

282. 74
289. 03
295. 31
301. 59
307. 88

6 361.7
6 647. 6

6 939. 8

7 238. 2
7 543.

7.162
7.321
7.480
7.639
7.799

161. 14
168. 39
175. 79
183. 35
191. 07

95

96
97
98
99

596.90
603. 19
609. 47
615. 75
622.04

28 353

28 953

29 559
30172

30 791

15 12
15 28
15.44
15.60
15.76

718. 19
733. 39
748. 74
764. 26
779. 94

50

314. 16

7 854.

7.958

198. 94
47r

100

628. 32

31416

15.92

795. 77

IS

'iirN

icm

2ir

u

2iri\r

Try*

2ir

±2n

4X

52

TABLE VI. -NATUML I'UNCTIONS

•

t

o°

1°^

2°

3^

4°

f

sin

cos

sin cos

sin

cos

sin

cos

sin

cos

0000

1.000

0175 9998

0349

9994

0523

9986

0698

9976

60

1

0003

1.000

0177 9998

0352

9994

0526

9986

0700

9975

59

2

0006

1.000

0180 9998

0355

9994

0529

9986

0703

9975

58

3

0009

1.000

0183 9998

0358

9994

0532

9986

0706

9975

57

4

0012

1.000

0186 9998

0361

9993

0535

9986

0709

9975

56

6

0015

1.000

0189 9998

0364

9993

0538

9986

0712

9975

55

6

0017

1.000

0192 9998

0366

9993

0541

9985

0715

9974

54

7

0020

1.000

0195 9998

0369

9993

0544

9985

0718

9974

53

8

0023

1.000

0198 9998

0372

9993

0547

9985

0721

9974

52

9

0026

1.000

0201 9998

0375

9993

0550

9985

0724

9974

51

lO

0029

1.000

0204 9998

0378

9993

C552

9985

0727

9974

50

11

0032

1.000

0207 9998

0381

9993

0555

9985

0729

9973

49

12

0035

1.000

0209 9998

0384

9993

0558

9984

0732

9973

48

13

0038

1.000

0212 9998

0387

9993

0561

9984

0735

9973

47

14

0041

1.000

0215 9998

0390

9992

0564

9984

0738

9973

46

15

0044

1.000

0218 9998

0393

9992

0567

9984

0741

9973

45

16

0047

1.000

0221 9998

0396

9992

0570

9984

0744

9972

44 .

17

0049

1.000

0224 9997

0398

9992

0573

9984

0747

9972

43

1«

0052

1.000

0227 9997

0401

9992

0576

9983

0750

9972

42

19

0055

1.000

0230 9997

0404

9992

0579

9983

0753

9972

41

20

0058

1.000

0233 9997

0407

9992

0581

9983

0756

9971

40

21

0061

1.000

0236 9997

0410

9992

0584

9983

0758

9971

39

22

0064

1.000

0239 9997

0413

9991

0587

9983

0761

9971

38

23

0067

1.000

0241 9997

0416

9991

0590

9983

0764

9971

37

24

0070

1.000

0244 9997

0419

9991

0593

9982

0767

9971

36

25

0073

1.000

0247 9997

0422

9991

0596

9982

0770

9970

35

26

0076

1.000

0250 9997

0425

9991

0599

9982

0773

9970

34

27

0079

1.000

0253 9997

0427

9991

0602

9982

0776

9970

33

28

0081

1.000

0256 9997

0430

9991

0605

9982

0779

9970

32

29

0084

1.000

0259 9997

0433

9991

0608

9982

0782

9969

31

30

0087

1.000

0262 9997

0436

9990

0610

9981

0785

9969

30

31

0090

1.000

0265 9996

0439

9990

0613

9981

0787

9969

29

32

0093

1.000

0268 9996

0442

9990

0616

9981

0790

9969

28

33

0096

1.000

0270 9996

0445

9990

0619

9981

0793

9968

27

34

0099

1.000

0273 9996

0448

9990

0622

9981

0796

9968

26

35

0102

9999

0276 9996

0451

9990

0625

9980

0799

9968

25

36

0105

9999

0279 9996

0454

9990

0628

9980

0802

9968

24

37

0108

9999

0282 9996

0457

9990

0631

9980

0805

9968

23

38

0111

9999

0285 9996

0459

9989

0634

9980

0808

9967

22

39

0113

9999

0288 9996

0462

9989

0637

9980

0811

9967

21

40

0116

9999

0291 9996

0465

9989

0640

9980

0814

9967

20

41

0119

9999

0294 9996

0468

9989

0642

9979

.0816

9967

19

42

0122

9999

0297 9996

0471

9989

0645

9979

0819

9966

18

43

0125

9999

0300 9996

0474

9989

0648

9979

0822

9966

17

44

0128

9999

0302 9995

0477

9989

0651

9979

0825

9966

16

45

0131

9999^

0305 9995

0480

9988

0654

9979

0828

9966

15

46

0134

9999

0308 9995

0483

9988

0657

9978

0831

9965

14

47

0137

9999

0311 9995

0486

9988

0660

9978

0834

9965

13

48

0140

9999

0314 9995

0488

9988

0663

9978

0837

9965

12

49

0143

9999

0317 9995

0491

9988

0666

9978

0840

9965

11

50

0145

9999

0320 9995

0494

9988

0669

9978

0843

9964

10

51

0148

9999

0323 9995

0497

9988

0671

9977

0845

9964

9

52

0151

9999

0326 9995

0500

9987

0674

9977

0848

9964

8

53

0154

9999

0329 9995

0503

9987

0677

9977

0851

9964

7

54

0157

9999

0332 9995

0506

9987

0680

9977

0854

9963

6

55

0160

9999

0334 9994

0509

9987

0683

9977

0857

9963

5

56

0163

9999

0337 9994

0512

9987

0686

9976

0860

9963

4

57

0166

9999

0340 9994

0515

9987

0689

9976

0863

9963

3

58

0169

9999

0343 9994

0518

9987

0692

9976

0866

9962

2

59

0172

9999

0346 9994

0520

9986

0695

9976

0869

9962

1

60

0175

9999

0349 9994

0523

9986

0698

9976

0872

9962

cos sin
89°

cos sin
88°

cos sin
87°

cos sin
86°

cos sin
85° •

t

f

NATTTRAL SINES AND COSINES.

58

/

5°

6°

70

8°

9°

t

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

0872

9962

1045

9945

1219

9925

1392

9903

1564

9877

60

1

0874

9962

1048

9945

1222

9925

1395

9902

1567

9876

59

2

0877

9961

1051

9945

1224

9925

1397

9902

1570

9876

58

3

0880

9961

1054

9944

1227

9924

1400

9901

1573

9876

57

4

0883

9961

1057

9944

1230

9924

1403

9901

1576

9875

56

5

0886

9961

1060

9944

1233

9924

1406

9901

1579

9875

55

6

0889

9960

1063

9943

1236

9923

1409

9900

1582

9874

54

7

0892

9960

1066

9943

1239

9923

1412

9900

1584

9874

S3

8

0895

9960

1068

9943

1241

9923

1415

9899

1587

9873

52

9

0898

9960

1071

9942

1245

9922

1418

9899

1590

9873

51

10

0901

9959

1074

9942

1248

9922

1421

9899

1593

9872

50

11

0903

9959

1077

9942

1250

9922

1423

9898

1596

9872

49

12

0906

9959

1080

9942

1253

9921

1426

9898

1599

9871

48

13

0909

9959

1083

9941

1256

9921

1429

9897

1602

9871

47

14

0912

9958

1086

9941

1259

9920

1432

9897

1605

9870

46

15

0915

9958

1089

9941

1262

9920

1435

9897

1607

9870

45

-16

0918

9958

1092

9940

1265

9920

1438

9896

1610

9869

44

17

0921

9958

1094

9940*

1268

9919

1441

9896

1613

9869

43

18

0924

9957

1097

9940

1271

9919

1444

9895

1616

9869

42

19

0927

9957

1100

9939

1274

9919

1446

9895

1619

9868

41

20

0929

9957

1103

9939

1276

9918

1449

9894

1622

9868

40

21

0932

9956

1106

9939

1279

9918

1452

9894

1625

9867

39

22

0935

9956

1109

9938

1282

9917

1455

9894

1628

9867

38

23

0938

9956

1112

9938

1285

9917

1458

9893

1630

9866

37

24

0941

9956

1115

9938

1288

9917

1461

9893

1633

9866

36

25

0944

9955

1118

9937

1291

9916

1464

9892

1636

9865

35

26

0947

9955

1120

9937

1294

9916

1467

9892

1639

9865

34

27

0950

9955

1123

9937

1297

9916

1469

9891

1642

9864

Zi

28

0953

9955

1126

9936

1299

9915

1472

9891

1645

9864

32

29

0956

9954

1129

9936

1302

9915

1475

9891

1648

9863

31

30

0958

9954

1132

9936

1305

9914

1478

9890

1650

9863

30

31

0961

9954

1135

9935

1308

9914

1481

9890

1653

9862

29

32

0964

9953

1138

9935

1311

9914

1484

9889

1656

9862

28

33

0967

9953

1141

9935

1314

9913

1487

9889

1659

9861

27

34

0970

9953

1144

9934

1317

9913

1490

9888

1662

9861

26

35

0973

9953

1146

9934

1320

9913

1492

9888

1665

9860

25

36

0976

9952

1149

9934

1323

9912

1495

9888

1668

9860

24

37

0979

9952

1152

9933

1325

9912

1498

9887

1671

9859

23

38

0982

9952

1155

9933

1328

9911

1501

9887

1673

9859

22

39

0985

9951

1158

9933

1331

9911

1504

9886

1676

9859

21

40

0987

9951

1161

9932

1334

9911

1507

9886

1679

9858

20

41

0990

9951

1164

9932

1337

9910

1510

9885

1682

9858

19

42

0993

9951

1167

9932

1340

9910

1513

9885

1685

9857

18

43

0996

9950

1170

9931

1343

9909

1515

9884

1688

9857

17

44

0999

9950

1172

9931

1346

9909

1518

9884

1691

9856

16

45

1002

9950

1175

9931

1349

9909

1521

9884

1693

9856

15

46

1005

9949

1178

9930

1351

9908

1524

9883

1696

9855

14

47

1008

9949

1181

9930

1354

9908

1527

9883

1699

9855

13

48

1011

9949

1184

9930

1357

9907

1530

9882

1702

9854

12

49

1013

9949

1187

9929

1360

9907

1533

9882

1705

9854

11

50

1016

9948

1190

9929

1363

9907

1536

9881

1708

9853

10

51

1019

9948

1193

9929

1366

9906

1538

9881

1711

9S53u

9

52

1022

9948

1196

9928

1369

9906

1541

9880

1714

9852

8

53

1025

9947

1198

9928

1372

9905

1544

9880

1716

9852

7

54

1028

9947

1201

9928

1374

9905

1547

9880

1719

9851

6

55

1031

9947

1204

9927

1377

9905

1550

9879

1722

9851

5

56

1034

9946

1207

9927

1380

9904

1553

9879

1725

9850

4

57

1037

9946

1210

9927

1383

9904

1556

9878

1728

9850

3

58

1039

9946

1213

9926

1386

9903

1559

9878

1731

9849

2

59

1042

9946

1216

9926

1389

9903

1561

9877

1734

9849

1

60

1045

9945

1219

9925

1392

9903

1564

9877

1736

9848

cos sin
84°

cos sin
83°

cos sin
82°

cos sin
81°

cos sin
80°

'

t

54

NATURAL SIN:ES AND COSINES.

/

10°

11°

12°

13°

14°

f

sin

cos

sin cos

sin

cos

sin cos

sin

cos

o

1736

9848

1908 9816

2079

9781

2250 9744

2419

9703

60

1

1739

9848

1911 9816

2082

9781

2252 9743

2422

9702

59

2

1742

9847

1914 9815

2085

9780

2255 9742

2425

9702

58

3

1745

9847

1917 9815

20S8

9780

2258 9742

2428

9701

57

4

1748

9846

1920 9814

2090

9779

2261 9741

2431

9700

56

5

1751

9846

1922 9813

2093

9778

2264 9740

2433

9699

55

6

1754

9845

1925 9813

2096

9778

2267 9740

2436

9699

54

7

1757

9845

1928 9812

2099

9777

2269 9739

2439

9698

53

8

1759

9844

1931 9812

2102

9777

2272 9738

2442

9697

52

9

1762

9843

1934 9811

2105

9776

2275 9738

2445

9697

51

lO

1765

9843

1937 9811

2108

9775

2278 9737

2447

9696

50

11

1768

9842

1939 9810

2110

9775

2281 9736

2450

9695

49

12

1771

9842

1942 9810

2113

9774

2284 9736

2453

9694

48

13

1774

9841

1945 9809

2116

9774

2286 9735

2456

9694

47

14

1777

9841

1948 9808

2119

9773

2289 9734

2459

9693

46

15

1779

9840

1951 9808

2122

9772

2292 9734

2462

969^

45

16

1782

9840

1954 9807

2125

9772

.2295 9733

2464

9692

44

17

1785

9839

1957 9807

2127

9771

2298 9732

2467

9691

43

18

1788

9839

1959 9806

2130

9770

2300 9732

2470

9690

42

19

1791

9838

1962 9806

2133

9770

2303 9731

2473

9689

41

20

1794

9838

1965 9805

2136

9769

2306 9730

2476

9689

40

21

1797

9837

1968 9804

2139

9769

2309 9730

2478

9688

39

22

1799

9837

1971 9804

2142

9768

2312 9729

2481

9687

38

23

1802

9836

1974 9803

2145

9767

2315 9728

2484

9687

37

24

1805

9836

1977 9803

2147

9767

2317 9728

2487

9686

36

25

1808

9835

1979 9802

2150

9766

2320 9727

2490

9685

35

26

1811

9835

1982 9802

2153

9765

2323 9726

2493

9684

34

27

1814

9834

1985 9801

2156

9765

2326 9726

2495

9684

33

28

1817

9834

1988 9800

2159

9764

2329 9725

2498

9683

32

29

1819

9833

1991 9800

2162

9764

2332 9724

2501

9682

31

30

1822

9833

1994 9799

2164

9763

2334 9724

2504

9681

30

31

1825

9832

1997 9799

2167

9762

2337 9723

2507

9681

29

32

1828

9831

1999 9798

2170

9762

2340 9722

2509

9680

28

33

1831

9831

2002 9798

2173

9761

2343 9722

2512

9679

27

34

1834

9830

2005 9797

2176

9760

2346 9721

2515

9679

26

35

1837

9830

2008 9796

2179

9760

2349 9720

2518

9678

25

36

1840

9829

2011 9796

2181

9759

2351 9720

2521

9677

24

37

1842

9829

2014 9795

2184

9759

2354 9719

2524

9676

23

38

1845

9828

2016 9795

2187

9758

2357 9718

2526

9676

22

39

1848

9828

2019 9794

2190

9757

2360 9718

2529

9675

21

40

1851

9827

2022 9793

2193

9757

2363 9717

2532

9674

20

41

1854

9827

2025 9793

2196

9756

2366 9716

2535

9673

19

42

1857

9826

2028 9792

2198

9755

2368 9715

2538

9673

18

43

1860

9826

2031 9792

2201

9755

2371 9715

2540

9672

17

44

1862

9825

2034 9791

2204

9754

2374 9714

2543

9671

16

45

1865

9825

2036 9790

2207

9753

2377 9713

2546

9670

15

46

1868

9824

2039 9790

2210

9753

2380 9713

2549

9670

14

47

1871

9823

2042 9789

2213

9752

2383 9712

2552

9669

13

48

1874

9823

2045 9789

2215

9751

2385 9711

2554

9668

12

49

1877

9822

2048 9788

2218

9751

2388 9711

2557

9667

11

50

1880

9822

2051 9787

2221

9750

2391 9710

2560

9667

lO

51

1882

9821

2054 9787

2224

9750

2394 9709

2563

9666

9

52

1885

9821

2056 9786

2227

9749

2397 9709

2566

9665

8

53

1888

9820

2059 9786

2230

9748

2399 9708

2569

9665

7

54

1891

9820

2062 9785

2233

9748

2402 9707

2571

9664

6

55

1894

9819

2065 9784

2235

9747

2405 9706

2574

9663

5

56

1897

9818

2068 9784

2238

9746

2408 9706

2577

9662

4

57

1900

9818

2071 9783

2241

9746

2411 9705

2580

9662

3

58

1902

9817

2073 9783

2244

9745

2414 9704

2583

9661

2

59

1905

9817

2076 9782

2247

9744

2416 9704

2585

9660

1

60

1908

9816

2079 9781

2250

9744

2419 9703

2588

9659

O

cos sin
79°

cos sin
78°

cos sin

77°

cos sin
76°

cos sin

75°

f

f

NATURAL SLtnCS AND COSINES.

55

/

15°

16°

17°

18°
sin cos

19°

t

sin

cos

sin

cos

sin

cos

sin

cos

2588

9659

2756

9613

2924

9563

3090

9511

3256

9455

60

1

2591

9659

2759

9612

2926

9562

3093

9510

3258

9454

59

2

2594

9658

2762

9611

2929

9561

3096

9509

3261

9453

58

3

2597

9657

2765

9610

2932

9560

3098

9508

3264

9452

57

4

2599

9656

2768

9609

2935

9560

3101

9507

3267

9451

56

6

2602

9655

2770

9609

2938

9559

3104

9506

3269

9450

65

6

2605

9655

2773

9608

2940

9558

3107

9505

3272

9449

54

7

2608

9654

2776

9607

2943

9557

3110

9504

3275

9449

53

8

2611

9653

2779

9606

2Q46

9556

3112

9503

3278

9448

52

9

2613

9652

2782

9605

2949

9555

3115

9502

3280

9447

51

10

2616

9652

2784

9605

2952

9555

3118

9502

3283

9446

50

11

2619

9651

2787

9604

2954

9554 '

3121

9501

3286

9445

49

12

2622

9650

2790

9603

2957

9553

3123

9500

3289

9444

48

13

2625

9649

2793

9602

2960

9552

3126

9499

3291

9443

47

14

2628

9649

2795

9601

2963

9551

3129

9498

3294

9442

46

16

2630

9648

2798

9600

2965

9550

3132

9497

3297

9441

45

16

2633

9647

2801

9600

2968

9549

3134

9496

3300

9440

44

17

2636

9646

2804

9599

2971

9548

3137

9495

3302

9439

43

18

2639

9646

2807

9598

2974

9548

3140

9494

3305

9438

42

19

2642

9645

2809

9597

2977

9547

3143

9493

3308

9437

41

20

2644

9644

2812

9596

2979

9546

3145

9492

3311

9436

40

21

2647

9643

2815

9596

2982

9545

3148

9492

3313

9435

39

22

2650

9642

2818

9595

2985

9544

3151

9491

3316

9434

38

23

2653

9642

2821

9594

2988

9543

3154

9490

3319

9433

37

24

2656

9641

2823

9593

2990

9542

3156

9489

3322

9432

36

25

2658

9640

2826

9592

2993

9542

3159

9488

3324

9431

36

26

2661

9639

2829

9591

2996

9541

3162

9487

3327

9430

34

27

2664

9639

2832

9591

2999

9540

3165

9486

3330

9429

ZZ

28

2667

9638

2835

9590

3002

9539

3168

9485

3333

9428

32

29

2670

9637

2837

9589

3004

9538

3170

9484

3335

9427

31

30

2672

9636

2840

9588

3007

9537

3173

9483

3338

9426

30

31

2675

9636

2843

9587

3010

9536

3176

9482

3341

9425

29

32

2678

9635

2846

9587

3013

9535

3179

9481

3344

9424

28

33

2681

9634

2849

9586

3015

9535

3181

9480

3346

9423

27

34

2684

9633

2851

9585

3018

9534

3184

9480

3349

9423

26

35

2686

9632

2854

9584

3021

9533

3187

9479

3352

9422

25

36

2689

9632

2857

9583

3024

9532

3190

9478

3355

9421

24

37

2692

9631

2860

9582

3026

9531

3192

9477

3357

9420

23

38

2695

9630

2862

9582

3029

9530

3195

9476

3360

9419

22

39

2698

9629

2865

9581

3032

9529

3198

9475

3363

9418

21

40

2700

9628

2868

9580

3035

9528

3201

9474

3365

9417

20

41

2703

9628

2871

9579

3038

9527

3203

9473

3368

9416

19

42

2706

9627

2874

9578

3040

9527

3206

9472

3371

9415

18

43

2709

9626

2876

9577

3043

9526

3209

9471

337 f

9414

17

44

2712

9625

2879

9577

3046

9525

3212

9470

3376

9413

16

45

2714

9625

2882

9576

3049

9524

3214

9469

3379

9412

15

46

2717

9624

2885

9575

3051

9523

3217

9468

3382

9411

14

47

2720

9623

2888

9574

3054

9522

3220

9467

3385

9410

13

48

2723

9622

2890

9573

3057

9521

3223

9466

3387

9409

12

49

2726

9621

2893

9572

3060

9520

3225

9466

3390

9408

11

50

2728

9621

2896

9572

3062

9520

3228

9465

3393

9407

lO

51

2731

9620

2899

9571

3065

9519

3231

9464

3396

9406

9

52

2734

9619

2901

9570

3068

9518

3234

9463

3398

9405

8

53

2737

9618

2904

9569

3071

9517

3236

9462

3401

9404

7

54

2740

9617

2907

9568

3074

9516

3239

9461

3404

9403

6

55

2742

9617

2910

9567

3076

9515

3242

9460

3407

9402

5

56

2745

9616

2913

9566

3079

9514

3245

9459

3409

9401

4

57

2748

9615

2915

9566

3082

9513

3247

9458

3412

9400

3

58

2751

9614

2918

9565

3085

9512

3250

9457

3415

9399

2

59

2754

9613

2921

9564

3087

9511

3253

9456

3417

9398

1

60

2756

9613

2924

9563

3090

9511

3256

9455

3420

9397

cos sin

74°

cos sin
73°

cos sin

72°

cos sin

71°

cos sin
70°

t

r

56

NATtTRAL SINES AND COSINES.

/

20°

21°

22°

23°

24°

t

sin

cos

sin

cos

sin

cos

sin

cos

sin cos

3420

9397

3584

9336

3746

9272

3907

9205

4067 9135

60

1

3423

9396

3586

9335

3749

9271

3910

9204

4070 9134

59

2

3426

9395

3589

9334

3751

9270

3913

9203

4073 9133

58

3

3428

9394

3592

9333

3754

9269

3915

9202

4075 9132

57

4

3431

9393

3595

9332

3757

9267

3918

9200

4078 9131

56

5

3434

9392

3597

9331

3760

9266

3921

9199

4081 9130

55

6

3437

9391

3600

9330

3762

9265

3923

9198

4083 9128

54

7

3439

9390

3603

9328

3765

9264

3926

9197

4086 9127

53

8

3442

9389

3605

9327

3768

9263

3929

9196

4089 9126

52

9

3445

9388

3608

9326

3770

9262

3931

9195

4091 9125

51

10

3448

9387

3611

9325 .

3773

9261

3934

9194

4094 9124

50

11

3450

9386

3614

9324

3776

9260

3937

9192

4097 9122

49

12

3453

9385

3616

9323

3778

9259

3939

9191

,4099 9121

48

13

3456

9384

3619

9322

3781

9258

3942

9190

4102 9120

47

14

3458

9383

3622

9321

3784

9257

3945

9189

4105 9119

46

15

3461

9382

3624

9320

3786

9255

3947

9188

4107 9118

45

16

3464

9381

3627

9319

3789

9254

3950

9187

4110 9116

44

17

3467

9380

3630

9318

3792

9253

3953

9186

4112 9115

43

18

3469

9379

3633

9317

3795

9252

3955

9184

4115 9114

42

19

3472

9378

3635

9316

3797

9251

3958

9183

4118 9113

41

20

3475

9377

■3638

9315

3800

9250

3961

9182

4120 9112

40

21

3478

9376

3641

9314

3803

9249

3963

9181

4123 9110

39

22

3480

9375

3643

9313

3805

9248

3966

9180

4126 9109

38

23

3483

9374

3646

9312

3808

9247

3969

9179

4128 9108

37

24

3486

9373

3649

9311

3811

9245

3971

9178

4131 9107

36

25

3488

9372

3651

9309

3813

9244

3974

9176

4134 9106

35

26

3491

9371

3654

9308

3816

9243

3977

9175

4136 9104

34

27

3494

9370

3657

9307

3819

9242

3979

9174

4139 9103

33

28

3497

9369

3660

9306

3821

9241

3982

9173

4142 9102

32

29

3499

9368

3662

9305

3824

9240

3985

9172

4144 9101

31

30

3502

9367

3665

9304

3827

9239

3987

9171

4147 9100

30

31

3505

9366

3668

9303

3830

9238

3990

9169

4150 9098

29

32

3508

9365

3670

9302

3832

9237

3993

9168

4152 9097

28

33

3510

9364

3673

9301

3835

9235

3995

9167

4155 9096

27

34

3513

9363

3676

9300

3838

9234

3998

9166

4158 9095

26

35

3516

9362

3679

9299

3840

9233

4001

9165

4160 9094

25

36

3518

9361

3681

9298

3843

9232

4003

9164

4163 9092

24

37

3521

9360

3684

9297

3846

9231

4006

9162

4165 9091

23

38

3524

9359

3687

9296

3848

9230

4009

9161

4168 9090

22

39

3527

9358

3689

9295

3851

9229

4011

9160

4171 9088

21

40

3529

9356

3692

9293

3854

9228

4014

9159

4173 9088

20

41

3532

9355

3695

9292

3856

9227

4017

9158

4176 9086

19

42

3535

9354

3697

9291

3859

9225

4019

9157

4179 9085

18

43

3537

9353

3700

9290

3862

9224

4022

9155

4181 9084

17

44

3540

9352

3703

9289

3864

9223

4025

9154

4184 9083

16

45

3543

9351

3706

9288

3867

9222

4027

9153

4187 9081

15

46

3546

9350

3708

9287

3870

9221

4030

9152

4189 9080

14

47

3548

9349

3711

9286

3872

9220

4033

9151

4192 9079

13

48

3551

9348

3714

9285

3875

9219

4035

9150

4195 9078

12

49

3554

9347

3716

9284

3878

9218

4038

9148

4197 9077

11

50

3557

9346

3719

9283

3881

9216

4041

9147

4200 9075

10

51

3559

9345

3722

9282

3883

9215

4043

9146

4202 9074

9

52

3562

9344

3724

9281

3886

9214

4046

9145

4205. 9073

8

53

3565

9343

3727

9279

3889

9213

4049

9144

4208 9072

7

54

3567

9342

3730

9278

3891

9212

4051

9143

4210 9070

6

55

3570

9341

3733

9277

3894

9211

4054

9141

4213 9069

5

56

3573

9340

3735

9276

3897

9210

4057

9140

4216 9068

4

57

3576

9339

3738

9275

3899

9208

4059

9139

4218 9067

3

58

3578

9338

3741

9274

3902

9207

4062

9138

4221 9066

2

59

3581

9337

3743

9273

3905

9206

4065

9137

4224 9064

1

60

3584

9336

3746

9272

3907

9205

4067

9135

4226 9063

cos sin
69°

cos sin
68°

cos sin
67°

cos sin
66°

cos sin
65°

t

f

NATURAL SINES AND COSINES.

57

/

25°

26°

sin cos

27°

28°

29°

r

sin

cos

sin

cos

sin

cos

sin

cos

o

4226

9063

4384 8988

4540

8910

4695

8829

4848

8746

60

1

4229

9062

4386 8987

4542

8909

4697

8828

4851

8745

59

2

4231

9061

4389 8985

4545

8907

4700

8827

4853

8743

58

3

4234

9059

4392 8984

4548

8906

4702

8825

4856

8742

57

4

4237

9058

4394 8983

4550

8905

4705

8824

4858

8741

56

5

4239

9057

4397 8982

4553

8903

4708

8823

4861

8739

55

6

4242

9056

4399 8980

4555

8902

4710

8821

4863

8738

54

7

4245

9054

4402 8979

4558

8901

4713

8820

4866

8736

53

8

4247

9053

4405 8978

4561

8899

4715

8819

4868

8735

52

9

4250

9052

4407 8976

4563

8898

4718

8817

4871

8733

51

10

4253

9051

4410 8975

4566

8897

4720

8816

4874

8732

50

11

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cos

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cos sin
62°

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60°

f

64°

f

58

NATURAL SINES AND COSINES.

/

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31°

32°

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33°

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34°

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5000

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3

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57

4

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5

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5312

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55

6

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54

7

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8

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9

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5616

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50

11

5028

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8555

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8463

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5618

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49

12

5030

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8554

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8462

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5621

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48

13

5033

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8552

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8460

5478

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5623

8269

47

14

5035

8640

5185

8551

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5480

8364

5626

8268

46

15

5038

8638

5188

8549

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8457

5483

8363

5628

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45

16

5040

8637

5190

8548

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5485

8361

5630

8264

44

17

5043

8635

5193

8546

5341

8454

5488

8360

5633

8263

43

18

5045

8634

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8545

5344

8453

5490

8358

5635

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42

19

5048

8632

5198

8543

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5493

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5638

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41

20

5050

8631

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5640

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40

21

5053

8630

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5498

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39

22

5055

8628

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38

23

5058

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37

24

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25

5063

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35

26

5065

8622

5215

8532

5363

8440

5510

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34

27

5068

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5218

8531

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8439

5512

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5657

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33

28

5070

8619

5220

8529

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8437

5515

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5659

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29

5073

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31

30

5075

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5664

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29

32

5080

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5669

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28

33

5083

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5380

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5527

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27

34

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26

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25

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5090

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37

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5536

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8230

23

38

5095

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8514

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8421

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22

39

5098

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8513

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8420

5541

8324

5686

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21

40

5100

8601

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20

41

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8417

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19

42

5105

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O

cos sin
69°

cos sin
58°

cos sin

57°

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56°

cos sin

55°

f

t

NATURAL SINES AND COSINES.

69

/

35°

36°

37°

38°

39°

t

sin

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sin

cos

sin

cos

sin

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56

5

5748

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55

6

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11

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47

14

5769

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5911

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46

16

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46

16

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44

17

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43

18

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19

5781

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22

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COB sin

54°

cos sin
53°

cos sin
52°

cos sin
51°

cos sin
50°

f

t

60

NATURAL SINES AND COSINES.

/

40°

41°

42°

43°

sin cos

44°

f

sin

cos

sin

cos

sin

cos

sin

cos

6428

7660

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7547

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7431

6820

7314

6947

7193

60

1.

6430

7659

6563

7545

6693

7430

6822

7312

6949

7191

59

2

6432

7657

6565

7543

6696

7428

6824

7310

6951

7189

58

3

6435

7655

6567

7541

6698

7426

6826

7308

6953

7187

57

4

6437

7653

6569

7539

6700

7424

6828

7306

6955

7185

56

6

6439

7651

6572

7538

6702

7422

6831

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6957

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65

6

6441

7649

6574

7536

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7420

6833

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6959

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54

7

6443

7647

6576

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7300

6961

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53

8

6446

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6578

7532

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52

9

6448

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6580

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6965

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51

10

6450

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6583

7528

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6967

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50

11

6452

7640

658!;

7526

6715

7410

6843

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6970

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49

12

6455

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6845

7290

6972

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48

13

6457

7636

6589

7522

6719

7406

6848

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6974

7167

47

14

6459

7634

6591

7520

6722

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6850

7286

6976

7165

46

15

6461

7632

6593

7518

6724

7402

6852

7284

6978

7163

46

16

6463

7630

65%

7516

6726

7400

6854

7282

6980

7161

44

17

6466

7629

6598

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6856

7280

6982

7159

43

18

6468

7627

6600

7513

6730

7396

6858

7278

6984

7157

42

19

6470

7625

6602

7511

6732

7394

6860

7276

6986

7155

41

20

6472

7623

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6734

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6862

7274

6988

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40

21

6475

7621

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7507

6737

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6865

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7151

39

22

6477

7619

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6739

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38

23

6479

7617

6611

7503

6741

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6869

7268

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37

24

6481

7615

6613

7501

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6997

7145

36

25

6483

7613

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7499

6745

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6873

7264

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7143

36

26

6486

7612

6617

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6875

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34

27

6488

7610

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33

28

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6879

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32

29

6492

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31

30

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30

31

6497

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29

32

6499

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6631

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6760

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28

33

6501

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27

34

6503

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26

35

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26

36

6508

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6769

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24

37

6510

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6771

7359

6898

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7024

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23

38

6512

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6773

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6900

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7026

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22

39

6514

7587

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6775

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6903

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7028

7114

21

40

6517

758S

6648

7470

6777

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20

41

6519

7583

6650

7468

6779

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6907

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7110

19

42

6521

7581

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7466

6782

7349

6909

7230

7034

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18

43

6523

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6911

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7036

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17

44

6525

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45

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6788

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6915

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16

46

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6661

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6790

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6917

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14

47

6532

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6792

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6919

7220

7044

7098

13

48

6534

7570

6665

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12

49

6536

7568

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11

60

6539*

7566

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10

51

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6928

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9

52

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8

53

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7

54

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55

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5

56

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4

57

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3

58

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2

59

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1

60

6561

7547

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7431

6820

7314

6947

7193

7071

7071

cos sin
49°

cos sin
48"

cos sin

470

cos sin
46°

cos sin
45°

f

f

NATURAL TANGENTS AND COTANGENTS. 61

t

0°

1^

2^

3°

40

t

tan cot

tan cot

tan

cot

tan

cot

tan

cot

o

0000 Infinite

0175 57.2900

0349

28.6363

0524

19.0811

0699

14.3007

60

1

0003 3437.75

0177 56.3506

0352

28.3994

0527

18.9755

0702

14.2411

59

2

0006 1718.87

0180 55.4415

0355

28.1664

0530

18.8711

0705

14.1821

58

3

0009 1145.92

0183 54.5613

0358

27.9372

0533

18.7678

0708

14.1235

57

4

0012 859.436

0186 53.7086

0361

27.7117

0536

18.6656

0711

14.0655

56

5

0015 687.549

0189 52.8821

0364

27.4899

0539

18.5645

0714

14.0079

55

6

0017 572.957

0192 52.0807

0367

27.2715

0542

18.4645

0717

13.9507

54

7

0020 491.106

0195 51.3032

0370

27.0566

0544

18.3655

0720

13.8940

53

8

0023 429.718

0198 50.5485

0373

26.8450

0547

18.2677

0723

138378

52

9

0026 381.971

0201 49.8157

0375

26.6367

0550

18.1708

0726

13.7821

51

10

0029 343.774

0204 49.1039

0378

26.4316

0553

18.0750

0729

13.7267

50

11

0032 312521

0207 48.4121

0381

26.2296

0556

17.9802

0731

13.6719

49

12

0035 286.478

0209 47.7395

0384

26.0307

0559

17.8863

0734

13.6174

48

13

0038 264.441

0212 47.0853

0387

25.8348

0562

17.7934

0737

13.5634 ,

47

14

0041 245.552

0215 46.4489

0390

25.6418

0565

17.7015

0740

13.5098

46

15

0044 229.182

0218 45.8294

0393

25.4517

0568

17.6106

0743

13.4566

i5

16

0047 214.858

0221 45.2261

0396

25.2644

0571

17.5205

0746

13.4039

44

17

0049-202.219

0224 44.6386

0399

25.0798

0574

17.4314

0749

13.3515

43

18

0052 190.984

0227 44.0661

0402

24.8978

0577

17.3432

0752

13.2996

42

19

0055 180.932

0230 43.5081

0405

24.7185

0580

17.2558

0755

13.2480

41

20

00=^8 171.885

0233 42.9641

0407

24.5418

0582

17.1693

0758

13.1969

40

21

0061 163.700

0236 42.4335

0410

24.3675

0585

17.0837

0761

13.1461

39

22

0064 156.259

0239 41.9158

0413

24.1957

0588

16.9990

0764

130958

38

23

0067 149.465

0241 41.4106

0416

24.0263

0591

16.9150

0767

13.0458

37

24

0070 143.237

0244 40.9174

0419

23.8593

0594

16.8319

0769

12.9962

36

25

0073 137.507

0247 40.4358

0422

23.6945

0597

16.7496

0772

12.9469

35

26

0076 132.219

0250 39.9655

0425

23.5321

0600

16.6681

0775

12.8981

34

27

0079 127.321

0253 39.5059

0428

23.3718

0603

16.5874

0778

12.8496

33

28

0081 122.774

0256 39.0568

0431

23.2137

0606

16.5075

0781

12.8014

32

29

0084 118.540

0259 38.6177

0434

23.0577

0609

16.4283

0784

12.7536

31

30

0087 114.589

0262 38.1885

0437

22.9038

0612

163499

0787

12.7062

30

31

0090 110.892

0265 37.7686

0440

22.7519

0615

16.2722

0790

12.6591

29

32

0093 107.426

0268 37.3579

0442

22.6020

0617

16.1952

0793

12.6124

28

3,2,

0096 104.171

0271 36.9560

0445

22.4541

0620

16.1190

0796

12.5660

27

34

0099 101.107

0274 36.5627

0448

22.3081

0623

16.0435

0799

12.5199

26

35

0102 98.2179

0276 36.1776

0451

22.1640

0626

15.9687

0802

12.4742

25

36

0105 95.4895

0279 35 8006

0454

22.0217

0629

15.8945

0805

12.4288

24

37

0108 92.9085

0282 35.4313

0457

21.8813

0632

15.8211

0808

12.3838

23

38

0111 90.4633

0285 35.0695

0460

21.7426

0635

15.7483

0810

12.3390

22

39

0113 88.1436

0288 34.7151

0463

21.6056

0638

15.6762

0813

12.2946

21

40

0116 85.9398

0291 34.3678

0466

21.4704

0641

15.6048

0816

12.2505

20

41

0119 83.8435

0294 34.0273

0469

21.3369

0644

15.5340

0819

12.2067

19

42

0122 81.8470

0297 33.6935

0472

21.2049

0647

15.4638

0822

12.1632

IS

43

0125 79.9434

0300 33.3662

0475

21.0747

0650

15.3943

0825

12.1201

17

44

0128 78.1263

0303 33.0452

0477

20.9460

0653

15.3254

0828

12.0772

16

45

0131 76.3900

0306 32.7303

0480

20.8188

0655

15.2571

0831

12.0346

15

46

0134 74.7292

0308 32.4213

0483

20.6932

0658

15.1893

0834

11.9923

14

47

0137 73.1390

0311 32.1181

0486

20.5691

0661

15.1222

0837

11.9504

13

48

0140 71.6151

0314 31.8205

0489

20.4465

0664

15.0557

0840

11.9087

12

49

0143 70.1533

0317 31.5284

0492

20.3253

0667

14.9898

0843

11.8673

11

50

0146 68.7501

0320 31.2416

0495

20.2056

0670

14.9244

0846

11.8262

10

51

0148 67.4019

0323 30.9599

0498

20.0872

0673

14.8596

0849

11.7853

9

52

0151 66.1055

0326 30.6833

0501

19.9702

0676

14.7954

0851

11.7448

8

53

0154 64.8580

0329 30.4116

0504

19.8546

0679

14.7317

0854

11.7045

7

54

0157 63.6567

0332 30.1446

0507

19.7403

0682

14.6685

0857

11.6645

6

55

0160 62.4992

0335 29.8823

0509

19.6273

0685

14.6059

0860

11.6248

5

56

0163 61.3829

0338 29.6245

0512

19.5156

0688

14.5438

0863

11.5853

4

57

0166 60.3058

0340 29.3711

0515

19.4051

0690

14.4823

0866

11.5461

3

58

0169 59.2659

0343 29.1220

0518

19.2959

0693

14.4212

0869

11.5072

2

59

0172 58.2612

0346 28.8771

0521

19.1879

0696

14.3607

0872

11.4685

1

60

0175 57.2900

0349 28.6363

0524

19.0811

0699

14.3007

0875

11.4301

cot tan

cot tan

cot

tan

cot

tan

cot

tan

'

89°

88°

87°

86°

85°

t

62 NATURAL TANGENTS AND COTANGENTS.

t

5°

6^

70

8°

9°

t

tan

cot

tan

cot

tan

cot

tan

cot

tan

cot

o

0875

11.4301

1051

9.5144

1228

8.1443

1405

7.1154

1584

6.3138

60

1

0878

11.3919

1054

9.4878

1231

8.1248

1408

7.1004

1587

6.3019

59

2

0881

11.3540

1057

9.4614

1234

8.1054

1411

7.0855

1590

6.2901

58

3

0884

11.3163

1060

9.4352

1237

8.0860

1414

7.0706

1593

6.2783

57

4

0887

11.2789

1063

9.4090

1240

8.0667

1417

7.0558

1596

6.2666

56

5

0890

11.2417

1066

9.3831

1243

8.0476

1420

7.O410

1599

6.2549

55

6

0892

11.2048

1069

9.3572

1246

8.0285

1423

7.0264

1602

6.2432

54

7

0895

11.1681

1072

9.3315

1249

8.0095

1426

7.0117

1605

6.2316

53

8

0898

11.1316

1075

9.3060

1251

7.9906

1429

69972

1608

6.2200

52

9

0901

11.0954

1078

9.2806

1254

7.9718

1432

6.9827

1611

6.2085

51

10

0904

11.0594

1080

9.2553

1257

7.9530

1435

6.9682

1614

6.1970

50

11

0907

11.0237

1083

9.2302

1260

7.9344

1438

6.9538

1617

6.1856

49

12

0910

10.9882

1086

9.2052

1263

7.9158

1441

6.9395

1620

61742

48

13

0913

10.9529

1089

9.1803

1266

7.8973

1444

6.9252

1623

6.1628

47

14

0916

10.9178

1092

9.1555

1269

7.8789

1447

6.9110

1626

61515

46

15

0919

10.8829

1095

9.1309

1272

7.8606

1450

6.8969

1629

6.1402

45

16

0922

10.8483

1098

9.1065

1275

7.8424

1453

6.8828

1632

6.1290

44

17

0925

10.8139

1101

9.0821

1278

7.8243

1456

6.8687

1635

61178

43

18

0928

10.7797

1104

9.0579

1281

7.8062

1459

6.8548

1638

61066

42

19

0931

10.7457

1107

9.0338

1284

7.7883

1462

6.8408

1641

6.0955

41

20

0934

10.7119

1110

9.0098

1287

7.7704

1465

6.8269

1644

6.0844

40

21

0936

10.6783

1113

8.9860

1290

7.7525

1468

6.8131 ■

1647

6.0734

39

22

0939

10.6450

1116

8.9623

1293

7.7348

1471

6.7994

1650

6.0624

38

23

0942

10.6118

1119

8.9387

1296

7.7171

1474

67856

1653

6.0514

37

24

0945

10.5789

1122

8.9152

1299

7.6996

1477

67720

1655

6.0405

36

25

0948

10.5462

1125

8.8919

1302

7.6821

1480

6.7584

1658

6.0296

35

26

0951

10.5136

1128

8.8686

1305

7.6647

1483

6.7448

1661

60188

34

27

0954

10.4813

1131

8.8455

1308

7.6473

1486

67313

1664

6.0080

33

28

0957

10.4491

1134

8.8225

1311

7.6301

1489

67179

1667

5.9972

32

29

0960

10.4172

1136

8.7996

1314

7.6129

1492

6.7045

1670

5.9865

31

30

0963

10.3854

1139

8.7769

1317

7.5958

1495

66912

1673

5.9758

30

31

0966

10.3538

1142

8.7542

1319

7.5787

1497

6.6779

1676

5.9651

29

32

0969

10.3224

1145

8.7317

1322

7.5618

1500

6.6646

1679

5.9545

28

33

0972

10.2913

1148

8.7093

1325

7.5449

1503

6.6514

1682

5.9439

27

34

0975

10.2602

1151

8.6870

1328

7.5281

1506

6.6383

1685

5.9333

26

35

0978

10.2294

1154

8.6648

1331

7.5113

1509

66252

1688

5.9228

25

36

0981

10.1988

1157

8.6427

1334

7.4947

1512

6.6122

1691

5.9124

24

37

0983

10.1683

1160

8.6208

1337

7.4781

1515

6.5992

1694

5.9019

23

38

0986

10.1381

1163

8.5989

1340

7.4615

1518

6.5863

1697

5.8915

22

39

0989

10.1080

1166

8.5772

1343

7.4451

1521

65734

1700

5.8811

21

40

0992

10.0780

1169

8.5555

1346

7.4287

1524

6.5606

1703

5.8708

20

41

0995

10.0483

1172

8.5340

1349

7.4124

1527

65478

1706

5.8605

19

42

0998

10.0187

1175

8.5126

1352

7.3962

1530

65350

1709

5.8502

18

43

1001

9.9893

1178

8.4913

1355

7.3800

1533

65223

1712

5.8400

17

44

1004

9.9601

1181

8.4701

1358

7.3639

1536

65097

1715

5.8298

16

45

1007

9.9310

1184

8.4490

1361

7.3479

1539

6.4971

1718

5.8197

15

46

1010

9.9021

1187

8.4280

1364

7.3319

1542

6.4846

1721

5.8095

14

47

1013

9.8734

1189

8.4071

1367

7.3160

1545

6.4721

1724

5.7994

13

48

1016

9.8448

1192

8.3863

1370

7.3002

1548

6.4596

1727

5.7894

12

49

1019

9.8164

1195

8.3656

1373

7.2844

1551

6.4472

1730

5.7794

11

50

1022

9.7882

1198

8.3450

1376

7.2687

1554

6.4348

1733

5.7694

10

51

1025

9.7601

1201

8.3245

1379

7.2531

1557

6.4225

1736

5.7594

9

52

1028

9.7322

1204

8.3041

1382

7.2375

1560

6.4103

1739

5.7495

8

53

1030

9.7044

1207

8.2838

1385

7.2220

1563

6.3980

1742

5.7396

7

54

1033

9.6768

1210

82636

1388

7.2066

1566

63859

1745

5.7297

6

55

1036

9.6499

1213

8.2434

1391

7.1912

1569

6.3737

1748

5.7199

5

56

1039

96220

1216

8.2234

1394

7.1759

1572

6.3617

1751

5.7101

4

57

1(H2

9.5949

1219

8.2035

1397

7.1607

1575

6.3496

1754

5.7004

3

58

1(H5

9.5679

1222

8.1837

1399

7.1455

1578

6.3376

1757

5.6906

2

59

1048

9.5411

1225

8.1640

1402

7.1304

1581

6.3257

1760

5.6809

1

60

1051

9.5144

1228

8.1443

1405

7.1154

1584

6.3138

1763

5.6713

cot tan
84°

cot tan
83°

cot tan
82°

cot tan
81°

cot tan
80°

f

/

NATURAL TANGENTS AND COTANGENTS. 68

F

10°

11°

12°

13°

14°

f

tan

cot

tan

cot

tan

cot

tan

cot

tan

cot

1763

5.6713

1944

5.1446

2126

4.7046

2309

4.3315

2493

4.0108

60

1

1766

5.6617

1947

5.1366

2129

4.6979

2312

4.3257

2496

4.0058

59

2

1769

5.6521

1950

5.1286

2132

4.6912

2315

4.3200

2499

4.0009

58

3

1772

5.6425

1953

5.1207

2135

4.6845

2318

4.3143

2503

3.9959

57

4

1775

5.6330

1956

5.1128

2138

4.6779

2321

4.3086

2506

3.9910

56

6

1778

5.6234

1959

5.1049

2141

4.6712

2324

4.3029

2509

3.9861

55

6

1781

5.6140

1962

5.0970

2144

4.6646

2327

4.2972

2512

3.9812

54

7

1784

5.6045

1965

5.0892

2147

4.6580

2330

4,2916

2515

3.9763

53

8

1787

5.5951

1968

5.0814

2150

4.6514

2333

4.2859

2518

3.9714

52

9

1790

5.5857

1971

5.0736

2153

4.6448

2336

4.2803

2521

3.9665

51

10

1793

5.5764

1974

5.0658

2156

4.6382

2339

4.2747

2524

3.9617

50

11

1796

5.5671

1977

5.0581

2159

4.6317

2342

4.2691

2527

3.9568

49

12

1799

5.5578

1980

5.0504

2162

4.6252

2345

4.2635

2530

3.9520

48

13

1802

5.5485

1983

5.0427

2165

4.6187

2349

4.2580

2533

3.9471

47

14

1805

5.5393

1986

5.0350

2168

4.6122

2352

4.2524

2537

3.9423

46

15

1808

5.5301

1989

5.0273

2171

4.6057

2355

4.2468

2540

3.9375

45

16

1811

5.5209

1992

5.0197

2174

4.5993

2358

4.2413

2543

3.9327

44

17

1814

5.5118

1995

5.0121

2177

4.5928

2361

4.2358

2546

3.9279

43

18

1817

5.5026

1998

5.0045

2180

4.5864

2364

4.2303

2549

3.9232

42

19

1820

5.4936

2001

4.9969

2183

4.5800

2367

4.2248

2552

3.9184

41

20

1823

5.4845

2004

4.9894

2186

4.5736

2370

4.2193

2555

3.9136

40

21

1826

5.4755

2007

4.9819

2189

4.5673

2373

4.2139

2558

3.9089

39

22

1829

5.4665

2010

4.9744

2193

4.5609

2376

4.2084

2561

3.9042

38

23

1832

5.4575

2013

4.9669

2196

4.5546

2379

4.2030

2564

3.8995

37

24

1835

5.4486

2016

^..9594

2199

4.5483

2382

4.1976

2568

3.8947

36

25

1838

5.4397

2019

4.9520

2202

4.5420

2385

4.1922

2571

3.8900

35

26

1841

5.4308

2022

4.9446

2205

4.5357

2388

4.1868

2574

3.8854

34

27

1844

5.4219

2025

4.9372

2208

4.5294

2392

4.1814

2577

3.8807

33

28

1847

5.4131

2028

4.9298

2211

4.5232

2395

4.1760

2580

3.8760

32

29

1850

5.4043

2031

4.9225

2214

4.5169

2398

4.1706

2583

3.8714

31

30

1853

5.3955

2035

4.9152

2217

4.5107

2401

4.1653

2586

3.8667

30

31

1856

5.3868

2038

4.9078

2220

4.5045

2404

4.1600

2589

3.8621

29

32

1859

5.3781

2941

4.9006

2223

4.4983

2407

4.1547

2592

3.8575

28

33

1862

5.3694

2044

4.8933

2226

4.4922

2410

4.1493

2595

3.8528

27

34

1865

5.3607

2047

4.8860

2229

4.4860

2413

4.1441

2599

3.8482

26

35

1868

5.3521

2050

4.8788

2232

4.4799

2416

4.1388

2602

3.8436

25

36

1871

5.3435

2053

4.8716

2235

4.4737

2419

4.1335

2605

3.8391

24

37

1874

5.3349

2056

4.8644

2238

4.4676

2422

4.1282

2608

3.8345

23

38

1877

5.3263

2059

4.8573

2241

4.4615

2425

4.1230

2611

3.8299

22

39

1880

5.3178

2062

4.8501

2244

4.4555

2428

4.1178

2614

3.8254

21

40

1883

5.3093

2065

4.8430

2247

4.4494

2432

4.1126

2617

3.8208

20

41

1887

5.3008

2068

4.8359

2251

4.4434

2435

4.1074

2620

3.8163

19

42

1890

5.2924

2071

4.8288

2254

4.4374

2438

4.1022

2623

3.8118

18

43

1893

5.2839

2074

4.8218

2257

4.4313

2441

4.0970

2627

3.8073

17

44

1896

5.2755

2077

4.8147

2260

4.4253

2444

4.0918

2630

3.8028

16

45

1899

5.2672

2080

4.8077

2263

4.4194

2447

4.0867

2633

3.7983

15

46

1902

5.2588

2083

4.8007

2266

4.4134

2450

4.0815

2636

3.7938

14

47

1905

5.2505

2086

4.7937

2269

4.4075

2453

4.0764

2639

3.7893

13

48

1908

5.2422

2089

4.7867

2272

4.4015

2456

4.0713

2642

3.7848

12

\9

1911

5.2339

2092

4.7798

2275

4.3956

2459

4.0662

2645

3.7804

11

50

1914

5.2257

2095

4.7729

2278

4.3897

2462

4.0611

2648

3.7760

10

51

1917

5.2174

2098

4.7659

2281

4.3838

2465

4.0560

2651

3.7715

9

52

1920

5.2092

2101

4.7591

2284

4.3779

2469

4.0509

2655

3.7671

8

53

1923

5.2011

2104

4.7522

2287

4.3721

2472

4.0459

2658

3.7627

7

54

1926

5.1929

2107

4.7453

2290

4.3662

2475

4.0408

2661

3.7583

6

55

1929

5.1848

2110

4.7385

2293

4.3604

2478

4.0358

2664

3.7539

5

56

1932

5.1767

2113

4.7317

2296

4.3546

2481

4.0308

2667

3.7495

4

57

1935

5.1686

2116

4.7249

2299

4.3488

2484

4.0257

2670

3.7451

3

58

1938

5.1606

2119

4.7181

2303

4.3430

2487

4.0207

2673

3.7408

2

59

1941

5.1526

2123

4.7114

2306

4.3372

2490

4.0158

2676

3.7364

1

60

1944

5.1446

2126

4.7046

2309

4.3315

2493

4.0108

2679

3.7321

cot tan
79°

cot tan
78°

cot tan

77°

cot tan
76°

cot tan

75°

t

f

64

NATtTRAL TANGENTS AND

COTANGENTS.

f

15^

16^

17°

18°

19°

f

tan

cot

tan

cot

tan

cot

tan

cot

tan

cot

2679

3.7321

2867

3.4874

3057

3.2709

3249

3.0777

3443

2.9042

60

1

2683

3.7277

2871

3.4836

3060

3.2675

3252

3.0746

3447

2.9015

59

2

2686

3.7234

2874

3.4798

3064

3.2641

3256

3.0716

3450

2.8987

58

3

2689

3.7191

2877

3.4760

3067

3.2607

3259

3.0686

3453

2.8960

57

4

2692

3.7148

2880

3.4722

3070

3.2573

3262

3.0655

3456

2.8933

56

5

2695

3.7105

2883

3.4684

3073

3.2539

3265

3.0625

3460

2.8905

56

6

2698

3.7062

2886

3.4646

3076

3.2506

3269

3 0595

3463

2.8878

54

7

2701

3.7019

2890

3.4608

3080

3.2472

3272

3.0565

3466

2.8851

53

8

270+

3.6975

2893

3.4570

3083

3.2438

3275

3.0535

3469

2.8824

52

9

270S

3.6933

2896

3.4533

3086

3.2405

3278

3.0505

3473

2.8797

51

10

2711

3.6891

2899

3.4495

3089

3.2371

3281

3.0475

3476

2.8770

50

11

2714

3.6848

2902

3.4458

3092

3.2338

3285

3.0H5

3479

2.8743

49

12

2717

3.6806

2905

3.4420

3096

3.2305

3288

3.0415

3482

2.8716

48

13

2720

3.6764

2908

3.4383

3099

3.2272

3291

3.0385

3486

2.8689

47

14

2723

3.6722

2912

3.4346

3102

3.2238

3294

3.0356

3489

2.8662

46

15

2726

3.6680

2915

3.4308

3105

3.2205

3298

3.0326

3492

2.8636

45

16

2729

3.6638

2918

3.4271

3108

3.2172

3301

3.0296

3495

2.8609

44

17

2733

3.6596

2921

3.4234

3111

3.2139

3304

3.0267

3499

2.8582

43

18

2736

3.6554

2924

3.4197

3115

3.2106

3307

3.0237

3502

2.8556

42

19

2739

3.6512

2927

3.4160

3118

3.2073

3310

3.0208

3505

2.8529

41

20

2742

3.6470

2931

3.4124

3121

3.2041

3314

3.0178

3508

2.8502

40

21

2745

3.6429

2934

3.4087

3124

3.2008

3317

3.0149

3512

2.8476

39

22

2748

3.6387

2937

3.4050

3127

3.1975

3320

3.0120

3515

2.8449

38

23

2751

3.6346

2940

3.4014

3131

3.1943

3323

3.0090

3518

2.8423

37

24

2754

3.6305

2943

3.3977

3134

3.1910

3327

3.0061

3522

2.8397

36

25

2758

3.6264

2946

3.3941

3137

3.1878

3330

3.0032

3525

2.8370

35

26

2761

3.6222

2949

3.3904

3140

3.1845

ZZZZ

3.0003

3528

2.8344

34

27

2764

3.6181

2953

3.3868

3143

3.1813

3336

2.9974

3531

2.8318

33

28

2767

3.6140

2956

3.3832

3147

3.1780

3339

2.9945

3535

2.8291

32

29

2770

3.6100

2959

3.3796

3150

3.1748

3343

2 9916

3538

2.8265

31

30

2773

3.6059

2962

3.3759

3153

3.1716

3346

2.9887

3541

2.8239

30

31

2776

3.6018

2%5

3.3723

3156

3.1684

3349

2.9858

3544

2.8213

29

32

2780

3.5978

2%8

3.3687

3159

3.1652

3352

2.9829

3548

2.8187

28

33

2783

3.5937

2972

3.3652

3163

3.1620

3356

2.9800

3551

2.8161

27

34

2786

3.5897

2975

3.3616

3166

3.1588

3359

2.9772

3554

2.8135

26

35

2789

3.5856

2978

3.3580

3169

3.1556

3362

2.9743

3558

2.8109

25

36

2^92

3.5816

2981

3.3544

3172

3.1524

3365

2.9714

3561

2.8083

24

37

2795

3.5776

2984

3.3509

3175

3.1492

3369

2.9686

3564

2.8057

23

38

2798

3.5736

2987

3.3473

3179

3.1460

3372

2.9657

3567

2.8032

22

39

2801

3.5696

2991

3.3438

3182

3.1429

3375

2.9629

3571

2.8006

21

40

2805

3.5656

2994

3.3402

3185

3.1397

3378

2.9600

3574

2.7980

20

41

2808

3.5616

2997

3.3367

3188

3.1366

3382

2.9572

3577

2.7955

19

42

2811

3.5576

3000

3.3332

3191

3.1334

3385

2.9544

3581

2.7929

18

43

2814

3.5536

3003

3.3297

3195

3.1303

3388

2.9515

3584

2.7903

17

44

2817

3.5497

3006

3.3261

3198

3.1271

3391

2.9487

3587

2.7878

16

45

2820

3.5457

3010

3.3226

3201

3.1240

3395

2.9459

3590

2.7852

15

46

2823

3.5418

3013

3.3191

3204

3.1209

3398

2.9431

3594

2.7827

14

47

2827

3.5379

3016

3.3156

3207

3.1178

3401

2.9403

3597

2.7801

13

48

2830

3.5339

3019

3.3122

3211

3.1146

3404

2.9375

3600

2.7776

12

49

2833

3.5300

3022

3.3087

3214

3.1115

3408

2.9347

3604

2.7751

11

50

2836

3.5261

3026

3.3052

3217

3.1084

3411

2.9319

3607

2.7725

lO

51

2839

3.5222

3029

3.3017

3220

3.1053

3414

2.9291

3610

2.7700

9

52

2842

3.5183

3032

3.2983

3223

3.1022

3417

2.9263

3613

2.7675

8

53

2845

3.5144

3035

3.2948

3227

3.0991

3421

2.9235

3617

2.7650

7

54

2849

3.5105

3038

3.2914

3230

3.0961

3424

2.9208

3620

2.7625

6

55

2852

3.5067

3041

3.2880

3233

3.0930

3427

2.9180

3623

2.7600

5

56

2855

3.5028

3045

3.2845

3236

3.0899

3430

2.9152

3627

2.7575

4

57

2858

3.4989

3048

3.2811

3240

3.0868

3434

2.9125

3630

2.7550

3

58

2861

3.4951

3051

3.2777

3243

3.0838

3437

2.9097

3633

2.7525

2

59

2864

3.4912

3054

3.2743

3246

3.0807

3440

2.9070

3636

2.7500

1

60

2867

3.4874

3057

3.2709

3249

3.0777

3443

2.9042

3640

2.7475

O

cot

tan

cot

tan

cot

tan

cot

tan

cot

tan

t

74°

73°

72°

71°

70°

t

NATtJRAL TAKGENTS AND

COTANGENTS.

65

f

20^

21°

22°

23°

24°

f

tan

cot

tan

cot

tan

cot

tan

cot

tan

cot

36+0

2.7475

3839

2.6051

4040

2.4751

4245

2.3559

4452

2.2460

60

1

3643

2.7450

3842

2.6028

4044

2.4730

4248

2.3539

4456

2.2443

59

2

3646

2.7425

3845

2.6006

4047

2.4709

4252

2.3520

4459

2.2425

58

3

3650

2.7400

3849

2.5983

4050

2.4689

4255

2.3501

4463

2.2408

57

4

3653

2.7376

3852

2.5961

4054

2.4668

4258

2.3483

4466

2.2390

56

5

3656

2.7351

3855

2.5938

4057

2.4648

4262

2.3464

4470

2.2373

55

6

3659

2.7326

3859

2.5916

4061

2.4627

4265

2.3445

4473

2.2355

54

7

3663

2.7302

3862

2.5893

4064

2.4606

4269

2.3426

4477

2.2338

53

8

3666

2.7277

3865

2.5871

4067

2.4586

4272

2.3407

4480

2.2320

52

9

3669

2.7253

3869

2.5848

4071

2.4566

4276

2.3388

4484

2.2303

51

10

3673

2.7228

3872

2.5826

4074

2.4545

4279

2.3369

4487

2.2286

50

11

3676

2.7204

3875

2.5804

4078

2.4525

4283

2.3351

4491

2.2268

49

12

3679

2.7179

3879

2.5782

4081

2.4504

4286

2.3332

4494

2.2251

48

13

3683

2.7155

3882

2.5759

4084

2.4484

4289

2.3313

4498

2.2234

47

14

3686

2.7130

3885

2.5737

4088

2.4464

4293

2.3294

4501

2.2216

46

16

3689

2.7106

3889

2.5715

4091

2.4443

4296

2.3276

4505

2.2199

45

16

3693

2.7082

3892

2.5693

4095

2.4423

4300

2.3257

4508

2.2182

44

17

3696

2.7058

3895

2.5671

4098

2.4403

4303

2.3238

4512

2.2165

43

18

3699

2.7034

3899

2.5649

4101

2.4383

4307

2.3220

4515

2.2148

42

19

3702

2.7009

3902

2.5627

4105

2.4362

4310

2.3201

4519

2.2130

41

20

3706

2.6985

3906

2.5605

4108

2.4342

4314

2.3183

4522

2.2113

40

21

3709

2.6961

3909

2.5533

4111

2.4322

4317

2.3164

4526

2.2096

39

22

3712

2.6937

3912

2.5561

4115

2.4302

4320

2.3146

4529

2.2079

38

23

3716

2.6913

3916

2.5539

4118

2.4282

4324

2.3127

4533

2.2062

37

24

3719

2.6889

3919

2.5517

4122

2.4262

4327

2.3109

4536

2.2045

36

25

3722

2.6865

3922

2.5495

4125

2.4242

4331

2.3090

4540

2.2028

36

26

3726

2.6841

3926

2.5473

4129

2.4222

4334

2.3072

4543

2.2011

34

27

3729

2.6818

3929

2.5452

4132

2.4202

4338

2.3053

4547

2.1994

33

28

3732

2.6794

3932

2.5430

4135

2.4182

4341

2.3035

4550

2.1977

32

29

3736

2.6770

3936

2.5408

4139

2.4162

4345

2.3017

4554

2.1960

31

30

3739

2.6746

3939

2.5386

4142

2.4142

4348

2.2998

4557

2.1943

30

31

3742

2.6723

3942

2.5365

4146

2.4122

4352

2.2980

4561

2.1926

29

32

3745

2.6699

3946

2.5343

4149

2.4102

4355

2.2962

4564

2.1909

28

33

3749

2.6675

3949

2.5322

4152

2.4083

4359

2.2944

4568

2.1892

27

34

3752

2.6652

3953

2.5300

4156

2.4063

4362

2.2925

4571

2.1876

26

35

3755

2.6628

3956

2.5279

4159

2.4043

4365

2.2907

4575

2.1859

25

36

3759

2.6605

3959

2.5257

4163

2.4023

4369

2.2889

4578

2.1842

24

37

3762

2.6581

3963

2.5236

4166

2.4004

4372

2.2871

4582

2.1825

23

38

3765

2.6558

3966

2.5214

4169

2.3984

4376

2.2853

4585

2.1808

22

39

3769

2.6534

3969

2.5193

4173

2.3964

4379

2.2835

4589

2.1792

21

40

3772

2.6511

3973

2.5172

4176

2.3945

4383

2.2817

4592

2.1775

20

41

3775

2.6488

3976

2.5150

4180

2.3925

4386

2.2799

4596

2.1758

19

42

3779

2.6464

3979

2.5129

4183

2.3906

4390

2.2781

4599

2.1742

18

43

3782

2.6441

3983

2.5108

4187

2.3886

4393

2.2763

4603

2.1725

17

44

3785

2.6418

3986

2.5086

4190

2.3867

4397

2.2745

4607

2.1708

16

45

3789

2.6395

3990

2.5065

4193

2.3847

4400

2.2727

4610

2.1692

15

46

3792

2.6371

3993

2.5044

4197

2.3828

4404

2.2709

4614

2.1675

14

47

3795

2.6348

3996

2.5023

4200

2.3808

4407

2.2691

4617

2.1659

13

48

3799

2.6325

4000

2.5002

4204

2.3789

4411

2.2673

4621

2.1642

12

49

3802

2.6302

4003

2.4981

4207

2.3770

4414

2.2655

4624

2.1625

11

50

3805

2.6279

4006

2.4960

4210

2.3750

4417

2.2637

4628

2.1609

10

51

3809

2.6256

4010

2.4939

4214

2.3731

4421

2.2620

4631

2.1592

9

52

3812

2.6233

4013

2.4918

4217

2.3712

4424

2.2602

4635

2.1576

8

53

3815

2.6210

4017

2.4897

4221

2.3693

4428

2.2584

4638

2.1560

7

54

3819

2.6187

4020

2.4876

4224

2.3673

4431

2.2566

4642

2.1543

6

55

3822

2.6165

4023

2.4855

4228

2.3654

4435

2.2549

4645

2.1527

6

56

3825

2 6142

4027

2.4834

4231

2.3635

4438

2.2531

4649

2.1510

4

57

3829

2.6119

4030

2.4813

4234

2.3616

4442

2.2513

4652

2.1494

3

58

3832

2 6096

4033

2.4792

4238

2.3597

4445

2.2496

4656

2.1478

2

59

3835

2.6074

4037

2.4772

4241

2.3578

4449

2.2478

4660

2.1461

1

60

3839

2.6051

4040

2.4751

4245

2.3559

4452

2.2460

4663

2.1445

1

cot tan
69°

cot tan
68°

cot tan
67°

cot tan
66°

cot tan
65°

t

t5t)

NATtJRAL TANGENTS AND

COTANGENTS.

/

25^

26°

27°

28°

29°

f

tan

cot

tan

cot

tan

cot

tan

cot

tan

cot

4663

2.1445

4877

2.0503

5095

1.9626

5317

1.8807

5543

1.8040

60

1

4667

2.1429

4881

2.0488

5099

1.9612

5321

1.8794

5547

1.8028

59

2

4670

2.1413

4885

2.0473

5103

1.9598

5325

1.8781

5551

1.8016

58

3

4674

2.1396

4888

2.0458

5106

1.9584

5328

1.8768

5555

1.8003

57

4

4677

2.1380

4892

2.0M3

5110

1.9570

5332

1.8755

5558

1.7991

56

5

46S1

2.1364

4895

2.0428

5114

1.9556

5336

1.8741

5562

1.7979

55

6

4684

2.1348

4899

2.0413

5117

1.9542

5340

1.8728

5566

1.7966

54

7

4688

2.1332

4903

2.0398

5121

1.9528

5343

1.8715

5570

1.7954

53

8

4691

2.1315

4906

2.0383

5125

1.9514

5347

1.8702

5574

1.7942

52

9

4695

2.1299

4910

2.0368

5128

1.9500

5351

1.8689

5577

1.7930

51

10

4699

2.1283

4913

2.0353

5132

1.9486

5354

1.8676

5581

1.7917

50

11

4702

2.1267

4917

2.0338

5136

1.9472

5358

1.8663

5585

1.7905

49

12

4706

2.1251

4921

2.0323

5139

1.9458

5362

1.8650

5589

1.7893

48

13

4709

2.1235

4924

2.0308

5143

1.9444

5366

1.8637

5593

1.7881

47

14

4713

2.1219

4928

2.0293

5147

1.9430

5369

1.8624

5596

1.7868

46

15

4716

2.1203

4931

2.0278

5150

i:9416

5373

1.8611

5600

1.7856

45

16

4720

2.1187

4935

2.0263

5154

1.9402

5377

1.8598

5604

1.7844

44

17

4723

2.1171

4939

2.0248

5158

1.9388

5381

1.8585

5608

1.7832

43

18

4727

2.1155

4942

2.0233

5161

1.9375

5384

1.8572

5612

1.7820

42

19

4731

2.1139

4946

2.0219

5165

1.9361

5388

1.8559

5616

1.7808

41

20

4734

2.1123

4950

2.0204

5169

1.9347

5392

1.8546

5619

1.7796

40

21

4738

2.1107

4953

2.0189

5172

1.9333

5396

1.8533

5623

1.7783

39

22

4741

2.1092

4957

2.0174

5176

1.9319

5399

1.8520

5627

1.7771

38

23

4745

2.1076

4960

2.0160

5180

1.9306

5403

1.8507

5631

1.7759

37

24

. 4748

2.1060

4964

2.0145

5184

1.9292

5407

1.8495

5635

1.7747

36

25

4752

2.1(H4

4968

2.0130

5187

1.9278

5411

1.8482

5639

1.7735

35

26

4755

2.1028

4971

2.0115

5191

1.9265

5415

1.8469

5642

1.7723

34

27

4759

2.1013

4975

2.0101

5195

1.9251

5418

1.8456

5646

1.7711

33

28

4763

2.0997

4979

2.0086

5198

1.9237

5422

1.8443

5650

1.7699

31

29

4766

2.0981

4982

2.0072

5202

1.9223

5426

1.8430

5654

1.7687

31

30

4770

2.0965

4986

2.0057

5206

1.9210

5430

1.8418

5658

1.7675

30

31

4773

2.0950

4989

2.0042

5209

1.9196

5433

1.8405

5662

1.7663

29

32

4777

2.0934

4993

2.0028

5213

1.9183

5437

1.8392

5665

1.7651

28

33

4780

2.0918

4997

2.0013

5217

1.9169

5441

1.8379

5669

1.7639

27

34

4784

2.0903

5000

1.9999

5220

1.9155

5445

1.8367

5673

1.7627

26

35

4788

2.0887

5004

1.9984

5224

1.9142

5448

1.8354

5677

1.7615

25

36

4791

2.0872

5008

1.9970

5228

1.9128

5452

1.8341

5681

1.7603

24

37

4795

2.0856

5011

1.9955

5232

1.9115

5456

1.8329

5685

1.7591

23

38

4798

2.0840

5015

1.9941

5235

1.9101

5460

1.8316

5688

1.7579

22

39

4802

2.0825

5019

1.9926

5239

1.9088

5464

1.8303

5692

1.7567

21

40

4806

2.0809

5022

1.9912

5243

1.9074

5467

1.8291

5696

1.7556

20

41

4809

2.0794

5026

1.9897

5246

1.9061

5471

1.8278

5700

1.7544

19

42

4813

2.0778

5029

1.9883

5250

1.9047

5475

1.8265

5704

1.7532

18

43

4816

2.0763

5033

1.9868

5254

1.9034

5479

1.8253

5708

1.7520

17

44

4820

2.0748

5037

1.9854

5258

1.9020

5482

1.8240

5712

1.7508

16

45

4823

2.0732

5040

1.9840

5261

1.9007

5486

1.8228

5715

1.7496

15

46

4827

2.0717

5044

1.9825

5265

1.8993

5490

1.8215

5719

1.7485

14

47

4831

2.0701

5048

1.9811

5269

1.8980

5494

1.8202

5723

1.7473

13

48

4834

2.0686

5051

1.9797

5272

1.8967

5498

1.8190

5727

1.7461

12

49

4838

2.0671

5055

1.9782

5276

1.8953

5501

1.8177

5731

1.7449

11

50

4841

2.0655

5059

1.9768

5280

1.8940

5505

1.8165

5735

1.7437

lO

51

4845

2.0640

5062

1.9754

5284

1.8927

5509

1.8152

5739

1.7426

9

52

4849

2.0625

5066

1.9740

5287

1.8913

5513

1.8140

5743

1.7414

8

53

4852

2.0609

5070

1.9725

5291

1.8900

5517

1.8127

5746

1.7402

7

54

4856

2.0594

5073

1.9711

5295

1.8887

5520

1.8115

5750

1.7391

6

55

4859

2.0579

5077

1.9697

5298

1.8873

5524

1.8103

5754

1.7379

5

56

4863

20564

5081

1.9683

5302

1.8860

5528

1.8090

5758

1.7367

4

57

4867

2.0549

5084

1.9669

5306

1.8847

5532

1.8078

5762

1.7355

3

58

4870

2.0533

5088

1.9654

5310

1.8834

5535

1.8065

5766

1.7344

2

59

4874

2.0518

5092

1.9640

5313

1.8820

5539

1.8053

5770

1.7332

1

60

4877

2.0503

5095

1.9626

5317

1.8807

5543

1.8040

5774

1.7321

f

cot tan
64°

cot tan
63°

cot tan
62°

cot tan
61°

cot tan
60°

J

NATURAL TANGENTS AND COTANGENTS. 6*1

t

30^

31°

32°

33°

34°

t

tan cot

tan

cot

tan

cot

tan

cot

tan

cot

5774 1.7321

6009

1.6643

6249

1.6003

6494

1.5399

6745

1.4826

60

1

5777 1.7309

6013

1.6632

6253

1.5993

6498

1.5389

6749

1.4816

59

2

5781 1.7297

6017

1.6621

6257

1.5983

6502

1.5379

6754

1.4807

58

3

5785 1.7286

6020

1.6610

6261

1.5972

6506

1.5369

6758

1.4798

■57

4

5789 1.7274

6024

1.6599

6265

1.5962

6511

1.5359

6762

1.4788

56

5

5793 1.7262

6028

1.6588

6269

1.5952

6515

1.5350

6766

1.4779

55

6

5797 1.7251

6032

1.6577

6273

1.5941

6519

1.5340

6771

1.4770

54

7

5801 1.7239

6036

1.6566

6277

1.5931

6523

1.5330

6775

1.4761

53

8

5805 1.7228

6040

1.6555

6281

1.5921

6527

1.5320

6779

1.4751

52

9

5808 1.7216

6044

1.6545

6285

1.5911

6531

1.5311

6783

1.4742

51

lO

5812 1.7205

6048

1.6534

6289

1.5900

6536

1.5301

6787

1.4733

50

11

5816 1.7193

6052

1.6523

6293

1.5890

6540

1.5291

6792

1.4724

49

12

5820 1.7182

6056

1.6512

6297

1.5880

6544

1.5282

6796

1.4715

48

13

5824 1.7170

6060

1.6501

6301

1.5869

6548

1.5272

6800

1.4705

47

14

5828 1.7159

6064

1.6490

6305

1.5859

6552

1.5262

6805

1.4696

46

15

5832 1.7147

6068

1.6479

6310

1.5849

6556

1.5253

6809

1.4687

45

16

5836 1.7136

6072

1.6469

6314

1.5839

6560

1.5243

6813

1.4678

44

17

5840 1.7124

6076

1.6458

6318

1.5829

6565

1.5233

6817

1.4669

43

18

5844 1.7113

6080

1.6447

6322

1.5818

6569

1.5224

6822

1.4659

42

19

5847 1.7102

6084

1.6436

6326

1.5808

6573

1.5214

6826

1.4650

41

20

5851 1.7090

6088

1.6426

6330

1.5798

6577

1.5204

6830

1.4641

40

21

5855 1.7079

6092

1.6415

6334

1.5788

6581

1.5195

6834

1.4632

39

22

5859 1.7067

6096

1.6404

6338

1.5778

6585

1.5185

6839

1.4623

38

23

5863 1.7056

6100

1.6393

6342

1.5768

6590

.1.5175

6843

1.4614

37

24

5867 1.7045

6104

1.6383

6346

1.5757

6594

1.5166

6847

1.4605

36

25

5871 1.7033

6108

1.6372

6350

1.5747

6598

1.5156

6851

1.4596

35

26

5875 1.7022

6112

1.6361

6354

1.5737

6602

1.5147

6856

1.4586

34

27

5879 1.7011

6116

1.6351

6358

1.5727

6606

1.5137

6860

1.4577

33

28

5883 1.6999

6120

1.6340

6363

1.5717

6610

1.5127

6864

1.4568

32

29

5887 1.6988

6124

1.6329

6367

1.5707

6615

1.5118

6869

1.4559

31

30

5890 1.6977

6128

1.6319

6371

1.5697

6619

1.5108

6873

1.4550

30

31

5894 1.6965

6132

1.6308

6375

1.5687

6623

1.5099

6877

1.4541

29

32

5898 1.6954

6136

1.6297

6379

1.5677

6627

1.5089

6881

1.4532

28

33

5902 1.6943

6140

1.6287

6383

1.5667

6631

1.5080

6886

1.4523

27

34

5906 1.6932

6144

1.6276

6387

1.5657

6636

1.5070

6890

1.4514

26

35

5910 1.6920

6148

1.6265

6391

1.5647

6640

1.5061

6894

1.4505

35

36

5914 1.6909

6152

1.6255

6395

1.5637

6644

1.5051

6899

1.4496

24

37

5918 1.6898

6156

1.6244

6399

1.5627

6648

1.5042

6903

1.4487

23

38

5922 1.6887

6160

1.6234

6403

1.5617

6652

1.5032

6907

1.4478

22

39

5926 1.6875

6164

1.6223

6408

1.5607

6657

1.5023

6911

1.4469

21

40

5930 1.6864

6168

1.6212

6412

1.5597

6661

1.5013

6916

1.4460

20

41

5934 1.6853

6172

1.6202

6416

1.5587

6665

1.5004

6920

1.4451

19

42

5938 1.6842

6176

1.6191

6420

1.5577

6669

1.4994

6924

1.4442

18

43

5942 1.6831

6180

1.6181

6424

1.5567

6673

1.4985

6929

1.4433

17

44

5945 1.6820

6184

1.6170

6428

1.5557

6678

1.4975

6933

1.4424

16

45

5949 1.6808

6188

1.6160

6432

1.5547

6682

1.4966

6937

1.4415

15

46

5953 1.6797

6192

1.6149

6436

1.5537

6686

1.4957

6942

1.4406

14

47

5957 1.6786

6196

1.6139

6440

1.5527

6690

1.4947

6946

1.4397

13

48

5961 1.6775

6200

1.6128

6445

1.5517

6694

1.4938

6950

1.4388

12

49

5965 ■ 1.6764

6204

1.6118

6449

1.5507

6699

1.4928

6954

1.4379

11

50

5969 1.6753

6208

1.6107

6453

1.5497

6703

1.4919

6959

1.4370

lO

51

5973 1.6742

6212

1.6097

6457

1.5487

6707

1.4910

6963

1.4361

9

52

5977 1.6731

6216

1.6087

6461

1.S477

6711

1.4900

6967

1.4352

8

53

5981 1.6720

6220

1.6076

6465

1.5468

6716

1.4891

6972

1.4344

7

54

5985 1.6709

6224

1.6066

6469

1.5458

6720

1.4882

6976

1.4335

6

55

5989 1.6698

6228

1.6055

6473

1.5448

6724

1.4872

6980

1.4326

5

56

5993 1.6687

6233

1.6045

6478

1.5438

6728

1.4863

6985

1.4317

4

57

5997 1.6676

6237

1.6034

6482

1.5428

6732

1.4854

6989

1.4308

3

58

6001 1.6665

6241

1.6024

6486

1.5418

6737

1.4844

6993

1.4299

2

59

6005 1.6654

6245

1.6014

6490

1.5408

6741

1.4835

6998

1.4290

1

60

6009 1.6643

6249

1.6003

6494

1.5399

6745

1.4826

7002

1.4281

O

cot tan

cot

tan

cot

tan

cot

tan

cot

tan

t

59°

58°

57°

56°

55°

t

68

NATURAL TANGENTS AND

COTANGENTS.

f

85°

36°

37°

38°

39°

t

tan

cot

tan

cot

tan

cot

tan

cot

tan

cot

7002

1.4281

7265

1.3764

7536

1.3270

7813

1.2799

8098

1.2349

60

1

7006

1.4273

7270

1.3755

7540

1.3262

7818

1.2792

8103

1.2342

59

2

7011

1.4264

7274

1.3747

7545

1.3254

7822

1.2784

8107

1.2334

58

3

7015

1.4255

7279

1.3739

7549

1.3246

7827

1.2776

8112

1.2327

57

4

7019

1.4246

7283

1.3730

7554

1.3238

7832

1.2769

8117

1.2320

56

5

7024

1.4237

7288

1.3722

7558

1.3230

7836

1.2761

8122

1.2312

66

6

7028

1.4229

7292

1.3713

7563

1.3222

7841

1.2753

8127

1.2305

54

7

7032

1.4220

7297

1.3705

7568

1.3214

7846

1.2746

8132

1.2298

53

8

7037

1.4211

7301

1.3697

7572

1.3206

7850

1.2738

8136

1.2290

52

9

7(H1

1.4202

7306

1.3688

7577

1.3198

7855

1.2731

8141

1.2283

51

10

7046

1.4193

7310

1.3680

7581

1.3190

7860

1.2723

8146

1.2276

60

11

7050

1.4185

7314

1.3672

7586

1.3182

7865

1.2715

8151

1.2268

49

12

7054

1.4176

7319

1.3663

7590

1.3175

7869

1.2708

8156

1.2261

48

13

7059

1.4167

7323

1.3655

7595

1.3167

7874

1.2700

8161

1.2254

47

14

7063

1.4158

7328

1.3647

7600

1.3159

7879

1.2693

8165

1.2247

46

15

7067

1.4150

7332

1.3638

7604

1.3151

7883

1.2685

8170

1.2239

46

16

7072

1.4141

7337

1.3630

7609

1.3143

7888

1.2677

8175

1.2232

44

17

7076

1.4132

7341

1.3622

7613

1.3135

7893

1.2670

8180

1.2225

43

18

7080

1.4124

7346

1.3613

7618

1.3127

7898

1.2662

8185

1.2218

42

19

7085

1.4115

7350

1.3605

7623

1.3119

7902

1.2655

8190

1.2210

41

20

7089

1.4106

7355

1.3597

7627

1.3111

7907

1.2647

8195

1.2203

40

21

7094

1.4097

7359

1.3588

7632

1.3103

7912

1.2640

8199

1.2196

39

22

7098

1.4089

7364

1.3580

7636

1.3095

7916

1.2632

8204

1.2189

38

23

7102

1.4080

7368

1.3572

7641

1.3087

7921

1.2624

8209

1.2181

37

24

7107

1.4071

7373

1.3564

7646

1.3079

7926

1.2617

8214

1.2174

36

26

7111

1.4063

7377

1.3555

7650

1.3072

7931

1.2609

8219

1.2167

35

26

7115

1.4054

7382

1.3547

7655

1.3064

7935

1.2602

8224

1.2160

34

27

7120

1.4045

7386

1.3539

7659

1.3056

7940

1.2594

8229

1.2153

33

28

7124

1.4037

7391

1.3531

7664

1.3048

7945

1.2587

8234

1.2145

32

29

7129

1.4028

7395

1.3522

7669

1.3040

7950

1.2579

8238

1.2138

31

30

7133

1.4019

7400

1.3514

7673

1.3032

7954

1.2572

8243

1.2131

30

31

7137

1.4011

7404

1.3506

7678

1.3024

7959

1.2564

8248

1.2124

29

32

7142

1.4002

7409

1.3498

7683

1.3017

7964

1.2557

8253

1.2117

28

33

7146

1.3994

7413

1.3490

7687

1.3009

7969

1.2549

8258

1.2109

27

34

7151

1.3985

7418

1.3481

7692

1.3001

7973

1.2542

8263

1.2102

26

35

7155

1.3976

7422

1.3473

7696

1.2993

7978

1.2534

8268

1.2095

25

36

7159

1.3968

7427

1.3465

7701

1.2985

7983

1.2527

8273

1.2088

24

37

7164

1.3959

7431

1.3457

7706

1.2977

7988

1.2519

8278

1.2081

23

38

7168

1.3951

7436

1.3449

7710

1.2970

7992

1.2512

8283

1.2074

22

39

7173

1.3942

7440

1.3440

7715

1.2962

7997

1.2504

8287

1.2066

21

40

7177

1.3934

7445

1.3432

7720

1.2954

8002

1.2497

8292

1.2059

20

41

7181

1.3925

7449

1.3424

7724

1.2946

8007

1.2489

8297

1.2052

19

42

7186

1.3916

7454

1.3416

7729

1.2938

8012

1.2482

8302

1.2045

18

43

7190

1.3908

7458

1.3408

7734

1.2931

8016

1.2475

8307

1.2038

17

44

7195

1.3899

7463

1.3400

7738

1.2923

8021

1.2467

8312

1.2031

16

45

7199

1.3891

7467

1.3392

7743

1.2915

8026

1.2460

8317

1.2024

15

46

7203

1.3882

7472

1.3384

7747

1.2907

8031

1.2452

8322

1.2017

14

47

7208

1.3874

7476

1.3375

7752

1.2900

8035

1.2445

8327

1.2009

13

48

7212

1.3865

7481

1.3367

7757

1.2892

8040

1.2437

8332

1.2002

12

49

7217

1.3857

7485

1.3359

7761

1.2884

8045

1.2430

8337

1.1995

11

50

7221

1.3848

7490

1.3351

7766

1.2876

8050

1.2423

8342

1.1988

10

51

7226

1.3840

7495

1.3343

7771

1.2869

8055

1.2415

8346

1.1981

9

52

7230

1.3831

7499

1.3335

7775

1.2861

8059

1.2408

8351

1.1974

8

53

7234

1.3823

7504

1.3327

7780

1.2853

8064

1.2401

8356

1.1967

7

54

7239

1.3814

7508

1.3319

7785

1.2846

8069

1.2393

8361

1.1960

6

65

7243

1.3806

7513

1.3311

7789

1.2838

8074

1.2386

8366

1.1953

6

56

7248

13798

7517

1.3303

7794

1.2830

8079

1.2378

8371

1.1946

4

57

7252

1.3789

7522

1.3295

7799

1.2822

8083

1.2371

8376

1.1939

3

58

7257

1.3781

7526

1.3287

7803

1.2815

8088

1.2364

8381

1.1932

2

59

7261

1.3772

7531

1.3278

7808

1.2807

8093

1.2356

8386

1.1925

1

60

7265

1.3764

7536

1.3270

7813

1.2799

8098

1.2349

8391

1.1918

O

t

cot tan

64°

cot tan
53°

cot tan
62°

cot tan
61°

cot tan
50°

t

NATURAL TANGENTS AND COTANGENTS. 60

f

40°

41°

42°

43°

44°

t

tan

cot

tan

cot

tan

cot

tan

cot

tan

cot

o

8391

1.1918

8693

1.1504

9004

1.1106

9325

1.0724

9657

1.0355

60

1

8396

1.1910

8698

1.1497

9009

1.1100

9331

1.0717

9663

1.0349

59

2

8401

1.1903

8703

1.1490

9015

1.1093

9336

1.0711

9668

1.0343

58

3

8406

1.1896

8708

1.1483

9020

1.1087

9341

1.0705

9674

1.0337

57

4

8411

1.1889

8713

1.1477

9025

1.1060

9347

1.0699

9679

1.0331

56

6

8416

1.1882

8718

1.1470

9030

1.1074

9352

1.0692

9685

1.0325

56

6

8421

1.1875

8724

1.1463

9036

1.1067

9358

1.0686

9691

1.0319

54

7

8426

1.1868

8729

1.1456

9041

1.1061

9363

1.0680

9696

1.0313

53

8

8431

1.1861

8734

1.1450

9046

1.1054

9369

1.0674

9702

1.0307

52

9

8436

1.1854

8739

1.1443

9052

1.1048

9374

1.0668

9708

1.0301

51

10

8441

1.1847

8744

1.1436

9057

1.1041

9380

1.0661

9713

1.0295

50

11

8446

1.1840

8749

1.1430

9062

1.1035

9385

1.0655

9719

1.0289

49

12

8451

1.1833

8754

1.1423

9067

1.1028

9391

1.0649

9725

1.0283

48

13

8456

1.1826

8759

1.1416

9073

1.1022

9396

1.0643

9730

1.0277

47

14

8461

1.1819

8765

1.1410

9078

1.1016

9402

1.0637

9736

1.0271

46

15

8466

1.1812

8770

1.1403

9083

1.1009

9407

1.0630

9742

1.0265

45

16

8471

1.1806

8775

1.1396

9089

1.1003

9413

1.0624

9747

1.0259

44

17

8476

1.1799

8780

1.1389

9094

1.0996

9418

1.0618

9753

1.0253

43

18

8481

1.1792

8785

1.1383

9099

1.0990

9424

1.0612

9759

1.0247

42

19

8486

1.1785

8790

1.1376

9105

1.0983

9429

1.0606

9764

1.0241

41

20

8491

1.1778

8796

1.1369

9110

1.0977

9435

1.0599

9770

1.0235

40

21

8496

1.1771

.8801

1.1363

9115

1.0971

9440

1.0593

9776

1.0230

39

22

8501

1.1764

8806

1.1356

9121

1.0964

9446

1.0587

9781

1.0224

38

23

8506

1.1757

8811

1.1349

9126

1.0958

9451

1.0581

9787

1.0218

37

24

8511

1.1750

8816

1.1343

9131

1.0951

9457

1.0575

9793

1.0212

36

25

8516

1.1743

8821

1.1336

9137

1.0945

9462

1.0569

9798

1.0206

35

26

8521

1.1736

8827

1.1329

9142

1.0939

9468

1.0562

9804

1.0200

34

27

8526

1.1729

8832

1.1323

9147

1.0932

9473

1.0556

9810

1.0194

ZZ

28

8531

1.1722

8837

1.1316

9153

1.0926

9479

1.0550

9816

1.0188

32

29

8536

1.1715

8842

1.1310

9158

1.0919

9484

1.0544

9821

1.0182

31

30

8541

1.1708

8847

1.1303

9163

1.0913

9490

1.0538

9827

1.0176

30

31

8546

1.1702

•8852

1.1296

9169

1.0907

9495

1.0532

9833

1.0170

29

32

8551

1.1695

8858

1.1290

9174

1.0900

9501

1.0526

9838

1.0164

28

33

8556

1.1688

8863

1.1283

9179

1.0894

9506

1.0519

9844

1.0158

27

34

8561

1.1681

8868

1.1276

9185

1.0888

9512

1.0513

9850

1.0152

26

35

8566

1.1674

8873

1.1270

9190

1.0881

9517

1.0507

9856

1.0147

25

36

8571

1.1667

8878

1.1263

9195

1.0875

9523

1.0501

9861

1.0141

24

37

8576

1.1660

8884

1.1257

9201

1.0869

9528

1.0495

9867

1.0135

23

38

8581

1.1653

8889

1.1250

9206

1.0862

9534

1.0489

9873

1.0129

22

39

8586

1.1647

8894

1.1243

9212

1.0856

9540

1.0483

9879

1.0123

21

40

8591

1.1640

8899

1.1237

9217

1.0850

9545

1.0477

9884

1.0117

20

41

8596

1.1633

8904

1.1230

9222

1.0843

9551

1.0470

9890

1.0111

19

42

8601

1.1626

8910

1.1224

9228

1.0837

9556

1.0464

9896

1.0105

18

43

8606

1.1619

8915

1.1217

9233

1.0831

9562

1.0458

9902

1.0099

17

44

8611

1.1612

8920

1.1211

9239

1.0824

9567

1.0452

9907

1.0094

16

45

8617

1.1606

8925

1.1204

9244

1.0818

9573

1.0446

9913

1.0088

15

46

8622

1.1599

8931

1.1197

9249

1.0812

9578

1.0440

9919

1.0082

14

47

8627

1.1592

8936

1.1191

9255

1.0805

9584

1.0434

9925

1.0076

13

48

8632

1.1585

8941

1.1184

9260

1.0799

9590

1.0428

9930

1.0070

12

49

8637

1.1578

8946

1.1178

9266

1.0793

9595

1.0422

9936

1.0064

11

50

8642

1.1571

8952

1.1171

9271

1.0786

9601

1.0416

9942

1.0058

lO

51

8647

1.1565

8957

1.1165

9276

1.0780

9606

1.0410

9948

1.0052

9

52

8652

1.1558

8962

1.1158

9282

1.0774

9612

1.0404

9954

1.0047

8

53

8657

1.1551

8967

1.1152

9287

1.0768

9618

1.0398

9959

1.0041

7

54

8662

1.1544

8972

1.1145

9293

1.0761

9623

1.0392

9965

1.0035

6

55

8667

1.1538

8978

1.1139

9298

1.0755

9629

1.0385

9971

1.0029

5

56

8672

1.1531

8983

1.1132

9303

1.0749

9634

1.0379

9977

1.0023

4

57

8678

1.1524

8988

1.1126

9309

1.0742

9640

1.0373

9983

1.0017

3

58

8683

1.1517

8994

1.1119

9314

1.0736

9646

1.0367

9988

1.0012

2

59

8688

1.1510

8999

1.1113

9320

1.0730

9651

1.0361

9994

1.0006

1

60

8693

1.1504

9004

1.1106

9325

1.0724

9657

1.0355

1.000

1.0000

»

cot tan
49^^

cot tan
48°

cot

tan

cot tan
46°

cot tan

45°

47°

/

70

TABLE VII.-

-TRAVERSE TABLE.

Bearing.

Distance 1.

Distance 2.

Distance 3.

Distance 4.

Distance 5.

Bearing.

O f

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

O f

OlS

1.000

0.004

2.000

0.009

3.000

0.013

4.000

0.017

5.000

0.022

89 45

30

1.000

0.009

2.000

0.017

3.000

0.026

4.000

0.035

5.000

0.04^

30

45

1.000

0.013

2.000

0.026

3.000

0.039

4.000

O052

5.000

0.065

15

1

1.000

0.017

2.000

0.035

3.000

O052

3.999

O070

4.999

0.087

89

15

1.000

0.022

2.000

0.044

2.999

0.065

3.999

0.087

4.999

0.109

45

30

1.000

0.026

1.999

0.052

2.999

0.079

3.999

O105

4.998

0131

30

45

1.000

0.031

1.999

0.061

2.999

0.092

3.998

0122

4.998

0153

15

2

0.999

0.035

1.999

0.070

2.998

O105

3.998

O140

4.997

0.174

88

15

0.999

0.039

1.998

0.079

2.998

0118

3.997

0157

4.996

0.196

45

30

0.999

0.044

1.998

0.087

2.997

0131

3.996

0174

4.995

0.218

30

45

0.999

0.048

1.998

0.096

2.997

0.144

3.995

0192

4.994

0.240

15

3

0.999

0.052

1.997

0105

2.996

0157

3.995

0.209

4.993

0.262

87

15

0.998

0.057

1.997

0113

2.995

O170

3.994

0227

4.992

0.283

45

30

0.998

0.061

1.996

0122

2.994

0.183

3.993

0244

4.991

0.305

30

45

0.998

0.065

1.996

0131

2.994

0196

3.991

0262

4.989

0.327

15

4

0.998

0.070

1.995

0.140

2.993

0.209

3.990

0.279

4.988

0.349

86

IS

0.997

0.074

1.995

0148

2.992

0222

3.989

0.296

4.986

0.371

45

30

0.997

0.078

1.994

0157

2.991

0235

3.988

0314

4.985

0.392

30

45

0.997

0.083

1.993

0166

2.990

0.248

3.986

0.331

4.983

0.414

15

6

0.996

0.087

1.992

0174

2.989

0261

3.985

0.349

4.981

0.436

85

IS

0.996

0.092

1.992

0183

2.987

0275

3.983

0.366

4.979

0.458

45

30

0.995

0096

1.991

0192

2.986

0.288

3.982

0383

4.977

0.479

30

45

0.995

0.100

1.990

0.200

2.985

O301

3.980

0.401

4.975

O501

15

6

0.995

0.105

1.989

O209

2.984

0.314

3.978

0.418

4.973

0.523

84

15

0.994

0.109

1.988

0218

2.982

0.327

3.976

0.435

4.970

0.544

45

30

0.994

0.113

1.987

0226

2.981

0.340

3.974

0.453

4.968

0.566

30

45

0.993

0.118

1.986

023S

2.979

0353

3.972

0.470

4.965

0588

15

7

0.993

0.122

1.985

0.244

2.978

0.366

3.970

0.487

4.963

0.609

83

15

0.992

0.126

1.984

0.252

2.976

0.379

3.968

O505

4.960

0.631

45

30

0.991

0.131

1.983

0.261

2.974

0.392

3.966

OS22

4.957

0.653

30

45

0.991

0.135

1.982

O270

2.973

0.405

3.963

0539

4.954

0.674

15

8

0.990

0.139

1.981

0.278

2.971

0.418

3.961

0557

4.951

0.696

82

15

0.990

0.143

1.979

0.287

2.969

0.430

3.959

0574

4.948

0717

45

30

0.989

0.148

1.978

0296

2.967

0.443

3.956

0591

4.945

0.739

30

45

0.988

0152

1.977

0.304

2.965

0456

3.953

0.608

4.942

0761

15

9

0.988

0.156

1.975

0313

2.963

0.469

3.951

0.626

4.938

0782

81

IS

0.987

0.161

1.974

0.321

2.961

0482

3.948

0.643

4.935

0.804

45

30

0.986

0.165

1.973

0.330

2.959

0.495

3.945

0.660

4.931

0.825

30

45

0.986

0.169

1.971

0.339

2.957

0.508

3.942

0.677

4.928

0.847

15

10

0.985

0.174

1.970

0.347

2.954

0521

3.939

0.695

4.924

0.868

80

15

0.984

0.178

1.968

0.356

2.952

0534

3.936

07^2

4.920

0.890

45

30

0.983

0.182

1.967

0.364

2.950

0547

3.933

0.729

4.916

0.911

30

45

0.982

0,187

1.965

0373

2.947

O560

3.930

0.746

4.912

0.933

15

11

. 0.982

0.191

1.963

0382

2.945

0572

3.927

0.763

4.908

0.954

79

15

0.981

0.19S

1.962

0.390

2.942

0.585

3.923

0.780

4.904

0975

45

30

0980

0.199

1.960

0.399

2.940

0.598

3.920

0797

4.900

0.997

30

45

0.979

0.204

1.958

0.407

2.937

611

3.916

0.815

4.895

1.018

15

12

0.978

0.208

1.956

0.416

2.934

0624

3.913

0832

4.891

1.040

78

15

0.977

0.212

1.954

0.424

2.932

0.637

3.909

0.849

4 886

1.061

45

30

0.976

0.216

1.953

0.433

2.929

0.649

3.905

0.866

4.881

1.082

30

45

0975

0.221

1.951

0.441

2.926

662

3.901

883

4.877

1.103

15

13

0974

0.225

1.949

0.450

2.923

0.675

3.897

0.900

4.872

1.125

77

15

0.973

0.229

1.947

0.458

2.920

0.688

3.894

0.917

4.867

1.146

45

30

0.972

0.233

1.945

0.467

2.917

O700

3.889

0.934

4.862

1.167

30

45

0971

0.238

1.943

0.475

2.914

0713

3.885

0951

4.857

1.188

15

14

0.970

0.242

1.941

0.484

2.911

0726

3.881

0.968

4.851

1.210

76

15

0.969

0.246

1.938

0.492

2.908

0738

3.877

0.985

4.846

1.231

45

30

0.968

0.250

1.936

0.501

2.904

0.751

3.873

1.002

4.841

1.252

30

45

0.967

0.255

1.934

O509

2.901

0764

3.868

1.018

4.835

1.273

15

15

0.966

0.259

1.932

0.518

2.898

0776

3.864

1.035

4.830

1.294

75

O f

Dep. Lat.
Distance 1.

Dep. Lat.
Distance 2.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

O f

Bearing.

Distance 3.

Distance 4.

Distance 5.

Bearing.

75°-90'

-

OP-

-15°

71

Bearing.

Distance 6.

Distance 7.

Distance 8.

Distance 9.

Distance 10.

Bearing.

o f

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

o t

015

6.000

0.026

7.000

0.031

8.000

0.035

9.000

0.039

10.000

0.044

89 45

30

6.000

0.052

7.000

0.061

8.000

0.070

9.000

0.079

10.000

0.087

30

45

5.999

0.079

6.999

0.092

7.999

0.105

8.999

0.118

9.999

0.131

15

1

5.999

0.105

6.999

0.122

7.999

0.140

8.999

0.157

9.999

0.175

89

15

5.999

0.131

6.998

0.153

7.998

0.175

8.998

0.196

9.998

0.218

45

30

5.998

0.157

6.998

0.183

7.997

0.209

8.997

0.236

9.997

0.262

30

45

5.997

0.183

6.997

0.214

7.996

0.244

8.996

0.275

9.995

0.305

15

2

5.996

0.209

6.996

0.244

7.995

0.279

8.995

0.314

9.994

0.349

88

15

5.995

0.236

6.995

0.275

7.994

0.314

8.993

0.353

9.992

0.393

45

30

5.994

0.262

6.993

0.305

7.992

0.349

8.991

0.393

9.991

0.436

30

45

5.993

0.288

6.992

0.336

7.991

0.384

8.990

0.432

9.989

0.480

15

3

5.992

0.314

6.990

0.366

7.989

0.419

8.988

0.471

9.986

0.523

87

15

5.990

0.340

6.989

0.397

7.987

0.454

8.986

0.510

9.984

0.567

45

30

5.989

0.366

6.987

0.427

7.985

0.488

8.983

0.549

9.981

0.611

30

45

5.987

0.392

6.985

0.458

7.983

0.523

8.981

0.589

9.979

0.654

15

4

5.985

0.419

6.983

0.488

7.981

0.558

8.978

0.628

9.976

0.698

86

15

5.984

0.445

6.981

0.519

7.978

0.593

8.975

0.667

9.973

0.741

45

30

5.982

0.471

6.978

0.549

7.975

0.628

8.972

0.706

9.969

0.785

30

45

5.979

0.497

6.976

0.580

7.973

0.662

8.969

0.745

9.966

0.828

15

5

5.977

0.523

6.973

0.610

7.970

0.697

8.966

0.784

9.962

0.872

85

15

5.975

0.549

6.971

0.641

7.966

0.732

8.962

0.824

9.958

0.915

45

30

5.972

0.575

6.968

0.671

7.963

0.767

8.959

0.863

9.954

0.959

30

45

5.970

0.601

6.965

0.701

7.960

0.802

8.955

0.902

9.950

1.002

15

6

5.967

0.627

6.962

0.732

7.956

0.836

8.951

0.941

9.945

1.045

84

15

5.964

0.653

6.958

0.762

7.952

0.871

8.947

0.980

9.941

1.089

45

30

5.961

0.679

6.955

0.792

7.949

0.906

8.942

1.019

9.936

1.132

30

45

5.958

0.705

6.951

0.823

7.945

0.940

8.938

1.058

9.931

1.175

15

7

5.955

0.731

6.948

0.853

7.940

0.975

8.933

1.097

9.926

1.219

83

15

5.952

0.757

6.944

0.883

7.936

1.010

8.928

1.136

9.920

1.262

45

30

5.949

0.783

6.940

0.914

7.932

1.044

8.923

1.175

9.914

1.305

30

45

5.945

0.809

6.936

0.944

7.927

1.079

8.918

1.214

9.909

1.349

15

8

5.942

O.S35

6.932

0.974

7.922

1.113

8.912

1.253

9.903

1.392

82

15

5.938

0.861

6.928

1.004

7.917

1.148

8.907

1.291

9.897

1.435

45

30

5.934

0.887

6.923

1.035

7.912

1.182

8.901

1.330

9.890

1.478

30

45

5.930

0.913

6.919

1.065

7.907

1.217

8.895

1.369

9.884

1.521

15

9

5.926

0.939

6.914

1.095

7.902

1.251

8.889

1.408

9.877

1.564

81

• IS

5.922

0.964

6.909

1.125

7.896

1.286

8.883

1.447

9.870

1.607

45

30

5.918

0.990

6.904

1.155

7.890

1.320

8.877

1.485

9.863

1.651

30

45

5.913

1.016

6.899

1.185

7.884

1.355

8.870

1.524

9.856

1.694

15

10

5.909

1.042

6.894

1.216

7.878

1.389

8.863

1.563

9.848

1.737

80

15

5.904

1.068

6.888

1.246

7.872

1.424

8.856

1.601

9.840

1.779

45

30

5.900

1.093

6.883

1.276

7.866

1.458

8.849

1.640

9.833

1.822

30

45

5.895

1.119

6.877

1.306

7.860

1.492

8.842

1.679

9.825

1.865

15

11

5.890

1.145

6.871

1.336

7.853

1.526

8.835

1.717

9.816

1.908

79

IS

5.885

1.171

6.866

1.366

7.846

1.561

8.827

1.756

9.808

1.951

45

30

5.880

1.196

6.859

1.396

7.839

1.595

8.819

1.794

9.799

1.994

30

45

5.874

1.222

6.853

1.425

7.832

1.629

8.811

1.833

9.791

2.036

15

12

5.869

1.247

6.847

1.455

7.825

1.663

8.803

1.871

9.782

2.079

78

15

5.863

1.273

6.841

1.485

7.818

1.697

8.795

1.910

9.772

2.122

45

30

5.858

1.299

6.834

1.515

7.810

1.732

8.787

1.948

9.763

2.164

30

45

5.852

1.324

6.827

1.545

7.803

1.766

8.778

1.986

9.753

2.207

15

13

5.846

1.350

6.821

1.575

7.795

1.800

8.769

2.025

9.744

2.250

77

15

5.840

1.375

6.814

1.604

7.787

1.834

8.760

2.063

9.734

2.292

45

30

5.834

1.401

6.807

1.634

7.779

1.868

8.751

2.101

9.724

2.335

30

45

5.828

1.426

6.799

1.664

7.771

1.902

8.742

2.139

9.713

2.377

15

14

5.822

1.452

6.792

1.693

7.762

1.935

8.733

2.177

9.703

2.419

76

15

5.815

1.477

6.785

1.723

7.754

1.969

8.723

2.215

9.692

2.462

45

30

5.809

1.502

6.777

1.753

7.745

2.003

8.713

2.253

9.682

2.504

30

45

5.802

1.528

6.769

1.782

7.736

2.037

8.703

2.291

9.671

2.546

15

15

5.796

1.553

6.761

1.812

7.727

2.071

8.693

2.329

9.659

2.588

75

O f

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

O f

Bearing.

Distance 6.

Distance 7.

Distance 8.

Distantee 9.

Distance 10.

Bearing,

76°-9Q°-

72

15°-

-30»

Bearing.

Distance 1.

Distance 2.

Distance 3.

Distance 4.

Distance 5.

Bearing.

O f

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

O f

16 15

0.965

0.263

1.930

0.526

2.894

0.789

3.859

1.052

4.824

1.315

74 45

30

0.964

0.267

1.927

0.534

2.891

0.S02

3.855

1.069

4.818

1.336

30

45

0.%2

0.271

1.925

0.543

2.887

0.814

3.850

1.086

4.812

1.357

15

16

0.961

0.276

1.923

0.551

2.884

0.827

3.845

1.103

4.806

1.378

74

15

0.960

0.280

1.920

0.560

2.880

0.839

3.840

1.119

4.800

1.399

45

30

0.959

0.284

1.918

0.568

2.876

0.852

3.835

1.136

4.794

1.420

30

45

0.958

0.288

1.915

0.576

2.873

0.865

3.830

1.153

4.788

1.441

15

17

0.956

0.292

1.913

0.585

2.869

0.877

3.825

1.169

4.782

1.462

73

15

0.955

0.297

1.910

0.593

2.865

0.890

3.820

1.186

4.775

1.483

45

30

0.954

0.301

1.907

0.601

2.861

0.902

3.815

1.203

4.769

1.504

30

45

0.952

0.305

1.905

0.610

2.857

0.915

3.810

1.220

4.762

1.524

15

18

0.951

0.309

1.902

0.618

2.853

0.927

3.804

1.236

4.755

1.545

72

15

0.950

0.313

1.899

0.626

2.849

0.939

3.799

1.253

4.748

1.566

45

30

0.948

0.317

1.897

0.635

2.845

0.952

3.793

1.269

4.742

1.587

30

45

0.947

0.321

1.894

0.643

2.841

0.964

3.788

1.286

4.735

1.607

15

19

0.946

0.326

1.891

0.651

2.837

0.977

3.782

1.302

4.728

1.628

71

15

0.944

0.330

1.888

0.659

2.832

0.989

3.776

1.319

4.720

1.648

45

30

0.943

0.334

1.885

0.668

2.828

1.001

3.771

1.335

4.713

1.669

30

45

0.941

0.338

1.882

0.676

2.824

1.014

3.765

1.352

4.706

1.690

15

20

0.940

0.342

1.879

0.684

2.819

1.026

3.759

1.368

4.698

1.710

70

15

0.938

0.346

1.876

692

2.815

1.038

3.753

1.384

4.691

1.731

45

30

0.937

0350

1.873

0.700

2.810

1.051

3.747

1.401

4.683

1.751

30

45

0.935

0.354

1.870

0.709

2.805

1.063

3.741

1.417

4.676

1.771

15

21

0.934

0.358

1.867

0.717

2.801

1.075

3.734

1.433

4.668

1.792

69

15

0.932

0.362

1.864

0.725

2.796

1.087

3.728

1.450

4.660

1.812

45

30

0.930

0.367

1.861

0.733

2.791

1.100

3.722

1.466

4.652

1.833

30

45

0.929

0.371

1.8S8

0.741

2.786

1.112

3.715

1.482

4.644

1.853

15

22

0.927

0.375

1.854

0.749

2.782

1.124

3.709

1.498

4.636

1.873

68

15

0.926

0.379

1.851

0.757

2.777

1.136

3.702

1.515

4.628

1.893

45

30

0.924

0.383

1.848

0.765

2.772

1.148

3.696

1.531

4.619

1.913

30

45

0.922

0.387

1.844

0.773

2.767

1.160

3.689

1.547

4.611

1.934

15

23

0.921

0.391

1.841

0.781

2.762

1.172

3.682

1.563

4.603

1.954

67

15

0.919

0.395

1.838

0.789

2.756

1.184

3.675

1.579

4.594

1.974

45

30

0.917

0.399

1.834

0.797

2.751

1.196

3.668

1.595

4.585

1.994

30

45

0.915

0.403

1.831

0.805

2.746

1.208

3.661

1.611

4.577

2.014

15

24

0.914

0.407

1.827

0.813

2.741

1.220

3.654

1.627

4.568

2.034

66

15

0.912

0.411

1.824

0.821

2.735

1.232

3.647

1.643

4.559

2.054

45

30

0.910

0.415

1.820

0.829

2.730

1.244

3.640

1.659

4.550

2.073

30

45

0.908

0.419

1.816

0.837

2.724

1.256

3.633

1.675

4.541

2.093

15

25

0.906

0.423

1.813

0.845

2.719

1.268

3.625

1.690

4.532

2.113

66

15

0.904

0.427

1.809

0.853

2.713

1.280

3.618

1.706

4.522

2.133

45

30

0.903

0.431

1.805

0.861

2.708

1.292

3.610

1.722

4.513

2.153

30

45

0.901

0.434

1.801

0.869

2.702

1.303

3.603

1.738

4.503

2.172

15

26

0.899

0.438

1.798

0.877

2.696

1.315

3.595

1.753

4.494

2.192

64

15

0.897

0.442

1.794

0.885

2.691

1.327

3.587

1.769

4.484

2.211

45

30

0.895

0.446

1.790

892

2.685

1.339

3.580

1.785

4.475

2.231

30

45

0.893

0.450

1.786

0.900

2.679

1.350

3.572

1.800

4.465

2.250

15

27

0.891

0.454

1.782

0.908

2.673

1.362

3.564

1.816

4.455

2.270

63

15

0.889

0.458

1.778

0.916

2.667

1.374

3.556

1.831

4.445

2.289

45

30

0.887

0.462

1.774

0.923

2.661

1.385

3.548

1.847

4.435

2.309

30

45

0.885

0.466

1.770

0.931

2.655

1.397

3.540

1.862

4.425

2.328

15

28

0.883

0.469

1.766

0.939

2.649

1.408

3.532

1.878

4.415

2.347

62

15

0.881

0.473

1.762

0.947

2.643

1.420

3.524

1.893

4.404

2.367

45

30

0879

0.477

1.758

0.954

2.636

1.431

3.515

1.909

4.394

2.386

30

45

0.877

0.481

1.753

0.962

2.630

1.443

3.507

1.924

4.384

2.405

15

29

0.875

0.485

1.749

0.970

2.624

1.454

3.498

1.939

4.373

2.424

61

15

0.872

0.489

1.745

0.977

2.617

1.466

3.490

1.954

4.362

2.443

45

30

0.870

0.492

1.741

0.985

2.611

1.477

3.481

1.970

4.352

2.462

30

45

0.868

0.496

1.736

0.992

2.605

1.489

3.473

1.985

4.341

2.481

15

30

0.866

0.500

1.732

1.000

2,598

1.500

3.464

2.000

4.330

2.500

60

o r

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

O f

Boaring.

Distance 1.

Distance 2.

Distance 8.

Distance 4.

Distance 5.

Bearing.

60^-76'

15°-

-30

78

Bearing-

Distance 6.

Distance 7.

Distance 8.

Distance 9.

Distance 10.

Bearing.

O f

Lat.

Dep.

Lat. Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

O f

16 15

5.789

1.578

6.754 1.841

7.718

2.104

8.683

2.367

9.648

2.630

74 45

30

5.782

1.603

6.745 1.871

7.709

2.138

8.673

2.405

9.636

2.672

30

45

5.775

1.629

6.737 1.900

7.700

2.172

8662

2.443

9.625

2.714

15

16

5.768

1.654

6.729 1.929

7.690

2.205

8.651

2.481

9.613

2.756

74

15

5.760

1.679

6.720 1.959

7.580

2.239

8.640

2.518

9.601

2.798

45

30

5.753

1.704

6.712 1.988

7.671

2.272

8.629

2.556

9.588

2.840

30

45

5.745

1.729

6.703 2.017

7.661

2.306

8.618

2.594

9.576

2.882

15

17

5.738

1.754

6.694 2.047

7.650

2.339

8.607

2.631

9.563

2.924

73

15

5.730

1.779

6.685 2.076

7.640

2.372

8.595

2.669

9.550

2.965

45

30

5.722

1.804

6.676 2.105

7.630

2.406

8.583

2.706

9.537

3.007

30

45

5.714

1.829

6.667 2.134

7.619

2.439

8.572

2.744

9.524

3.049

15

18

5.706

1.854

6.657 2.163

7.608

2.472

8.560

2.781

9.511

3.090

72

15

5.698

1.879

6.648 2.192

7.598

2.505

8.547

2.818

9.497

3.132

45

30

5.690

1.904

6.638 2.221

7.587

2,538

8.535

2,856

9.483

3.173

30

45

5.682

1.929

6.629 2.250

7.575

2.572

8.522

2.893

9.469

3.214

15

19

5.673

1.953

6.619 2.279

7.564

2.605

8.510

2,930

9.455

3.256

71

15

5.665

1.978

6.609 2.308

7.553

2.638

8.497

2.967

9.441

3.297

45

30

5.656

2.003

6.598 2.337

7.541

2.670

8.484

3.004

9.426

3.338

30

45

5.647

2.028

6.588 2.365

7.529

2.703

8.471

3.041

9.412

3.379

15

20

5.638

2.052

6.578 2.394

7.518

2.736

8.457

3.078

9.397

3.420

70

IS

5.629

2.077

6.567 2.423

7.506

2.769

8.444

3.115

9.382

3.461

45

30

5.620

2.101

6.557 2.451

7.493

2.802

8.430

3.152

9.367

3.502

30

45

5.611

2.126

6.546 2.480

7.481

2.834

8.416

3.189

9.351

3.543

15

21

5.601

2.150

6.535 2.509

7.469

2.867

8.402

3.225

9.336

3.584

69

15

5.592

2.175

6.524 2.537

7.456

2.900

8.388

3.262

9.320

3.624

45

30

5.582

2.199

6.513 2.566

7.443

2.932

8.374

3.299

9.304

3.665

30

45

5.573

2.223

6.502 2.594

7.430

2.964

8.359

3.335

9.288

3.706

15

22

S.563

2.248

6.490 2.622

7.417

2.997

8.345

3.371

9.272

3.746

68

15

5.553

2.272

6.479 2.651

7.404

3.029

8.330

3.408

9.255

3.787

45

30

5.543

2.296

6.467 2.679

7.391

3.061

8315

3.444

9.239

3.827

30

45

5.533

2.320

6.455 2.707

7.378

3.094

8.300

3.480

9.222

3.867

15

23

5.523

2.344

6.444 2.735

7.364

3.126

8.285

3.517

9.205

3.907

67

15

5.513

2.368

6.432 2.763

7.350

3.158

8.269

3.553

9.188

3.947

45

30

5.502

2.392

6.419 2.791

7.336

3.190

8.254

3.589

9,171

3.988

30

45

5.492

2.416

6.407 2.819

7.322

3.222

8.238

3.625

9.153

4.028

15

24

5.481

2.440

6.395 2.847

7.308

3.254

8.222

3.661

9.136

4.067

66

15

5.471

2.464

6.382 2.875

7.294

3.286

8.206

3.696

9.118

4.107

45

30

5.460

2.488

6.370 2.903

7.280

3.318

8.190

3.732

9.100

4.147

30

45

5.449

2.512

6.357 2.931

7.265

3.349

8.173

3.768

9,081

4.187

15

26

5.438

2.536

6.344 2.958

7.250

3.381

8.157

3.804

9.063

4.226

65

IS

5.427

2.559

6.331 2.986

7.236

3.413

8,140

3,839

9.045

4.266

45

30

5.416

2.583

6.318 3.014

7.221

3.444

8.123

3,875

9.026

4.305

30

45

5.404

2.607

6.305 3.041

7.206

3.476

8.106

3.910

9.007

4.345

15

26

5.393

2.630

6.292 3.069

7.190

3.507

8.089

3.945

8.988

4.384

64

15

5.381

2.654

6.278 3.096

7.175

3.538

8.072

3.981

8.969

4.423

45

30

5.370

2.677

6.265 3 123

7.160

3.570

8.054

4.016

8.949

4.462

30

45

5.358

2.701

6.251 3.151

7.144

3.601

8.037

4.051

8.930

4.501

15

2T

5.346

2.724

6.237 3.17S

7.128

3.632

8.019

4.086

8910

4.540

63

15

5.334

2.747

6.223 3.205

7.112

3.663

8.001

4.121

8.890

4.579

45

30

5.322

2.770

6.209 3.232

/ .096

3.694

7.983

4.156

8.870

4.618

30

45

5.310

2.794

6.195 3.259

7.080

3.725

7.965

4.190

8.850

4.656

15

28

5.298

2.817

6.181 3.286

7.064

3.7.56

7.947

4.225

8.829

4.695

62

15

5.285

2.840

6.166 3.313

7.047

3.787

7.928

4.260

8.809

4.733

45

30

5.273

2.863

6.152 3.340

7.031

3.817

7.909

4.294

8.788

4.772

30

45

5.260

2.886

6.137 3.367

7.014

3.848

7.891

4.329

8.767

4.810

15

29

5.248

2.909

6.122 3.394

6.997

3.878

7.872

4.363

8.746

4.848

61

15

5.235

2.932

6.107 3.420

6.980

3.909

7.852

4.398

8.725

4.886

45

30

5.222

2.955

6.093 3.447

6.963

3.939

7.833

4.432

8.704

4.924

30

45

5.209

2.977

6.077 3.474

6.946

3.970

7.814

4.466

8.682

4.962

15

30

5.196

3.000

6.062 3.500

6928

4.000

7.794

4.500

8.660

5.000

60

O f

Dep.

Lat.

Dep. Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

o t

Bearing.

Distance 6.

Distance 1 .

Distance 8.

Distance 9.

Distance 10.

Bearing.

60° -75'

74

30°-

-45

Bearing.

Distance 1.

Distance 2.

Distance 3.

Distance 4.

Distance 5.

Bearing.

o t

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

o /

3015

0.864

0.504

1.728

1.008

2.592

1.511

3.455

2.015

4.319

2.519

59 45

30

0.862

0.508

1.723

1.015

2.585

1.523

3.447

2.030

4.308

2.538

30

45

0.859

0.511

1.719

1.023

2.578

1.534

3.438

2.045

4.297

2 556

15

31

0.857

0.515

1.714

1.030

2.572

1.545

3.429

2,060

4.286

2.575

59

15

0.855

0.519

1.710

1.038

2.565

1.556

3.420

2.075

4.275

2.594

45

30

0.853

0.522

1.705

1.045

2.558

1.567

3.411

2.090

4.263

2612

30

45

0.850

0.526

1.701

1.052

2.551

1.579

3.401

2.105

4.252

2,631

15

32

0.848

0.530

1.696

1.060

2.544

1.590

3.392

2.120

4.240

2,650

58

15

0.846

0.534

1.691

1.067

2.537

1.601

3.383

2.134

4.229

2.668

45

30

0.843

0.537

1.687

1.075

2.530

1.612

3.374

2.149

4.217

2.686

30

45

0.841

0.541

1.682

1.082

2.523

1.623

3.364

2.164

4.205

2.705

15

33

0.839

0.545

1.677

1.089

2.516

1.634

3.355

2.179

4.193

2.723

57

15

0.836

0.548

1.673

1.097

2.509

1.645

3.345

2.193

4.181

2.741

45

30

0.834

0.552

1.668

1.104

2.502

1.656

3.336

2.208

4.169

2.760

30

45

0.831

0.556

1.663

1.111

2.494

1.667

3.326

2.222

4.157

2.778

15

34

0.829

0.559

1.658

1.118

2.487

1.678

3.316

2.237

4.145

2.796

56

15

0.827

0.563

1.653

1.126

2.480

1.688

3.306

2.251

4.133

2.814

45

30

0.824

0.566

1.648

1.133

2.472

1.699

3.297

2.266

4.121

2.832

30

45

0.822

0.570

1.643

1.140

2.465

1.710

3.287

2.280

4.108

2.850

15

35

0.819

0.574

1.638

1.147

2.457

1.721

3.277

2.294

4.096

2,868

55

15

0.817

0.577

1.633

1.154

2.450

1.731

3.267

2.309

4.083

2.886

45

30

0.814

0.581

1.628

1.161

2.442

1.742

3.257

2.323

4.071

2.904

30

45

0.812

0.584

1.623

1.168

2.435

1.753

3.246

2.337

4.058

2.921

15

36

0.809

0,588

1.618

1.176

2.427

1.763

3.236

2.351

4.045

2.939

54

15

0.806

0.591

1.613

1.183

2.419

1.774

3.226

2.365

4.032

2.957

45

30

0.8(H

0.595

1.608

1.190

2.412

1.784

3.215

2.379

4.019

2.974

30

45

0.801

0.598

1.603

1.197

2.404

1.795

3.205

2.393

4.006

2.992

15

37

0.799

0.602

1.597

1.204

2.396

1.805

3.195

2.407

3.993

3.009

53

15

0.796

0.605

1.592

1.211

2.388

1.816

3.184

2.421

3.980

3.026

45

30

0.793

0.609

1.587

1.218

2.380

1.826

3.173

2.435

3.967

3.044

30

45

0.791

0.612

1.581

1.224

2.372

1.837

3.163

2.449

3.953

3.061

15

38

0.788

0.616

1.576

1.231

2.364

1.847

3.152

2.463

3.940

3.078

52

15

0.785

0.619

1.571

1.238

2.356

1.857

3.141

2.476

3.927

3.095

45

30

0.783

0.623

1.565

1.245

2.348

1.868

3.130

2.490

3.913

3.113

30

45

0.780

0.626

1.560

1.252

2.340

1.878

3.120

2.504

3.899

3.130

15

39

0.777

0.629

1.554

1.259

2.331

1.888

3.109

2.517

3.886

3.147

51

15

0.774

0.633

1.549

1.265

2.323

1.898

3.098

2.531

3.872

3.164

45

30

0.772

0.636

1.543

1.272

2.315

1.908

3.086

2.544

3.858

3.180

30

45

0.769

0.639

1.538

1.279

2.307

1.918

3.075

2.558

3.844

3.197

15

40

0.766

0.643

1.532

1.286

2.298

1.928

3.064

2.571

3.830

3.214

50

15

0.763

0.646

1.526

1.292

2.290

1.938

3.053

2.584

3.816

3.231

45

30

0.760

0.649

1.521

1.299

2.281

1.948

3.042

2.598

3.802

3.247

30

45

0.758

0.653

1.515

1.306

2.273

1.958

3.030

2.611

3.788

3.264

15

41

0.755

0.656

1.509

1.312

2.264

1.968

3.019

2.624

3.774

3.280

49

15

0.752

0.659

1.504

1.319

2.256

1.978

3.007

2.637

3.759

3.297

45

30

0.749

0.663

1.498

1.325

2.247

1.988

2.996

2.650

3.745

3.313

30

45

0.746

0.666

1.492

1.332

2.238

1.998

2.984

2.664

3.730

3.329

15

42

0.743

0.669

1.486

1.338

2.229

2.007

2.973

2.677

3.716

3.346

48

15

0.740

0.672

1.480

1.345

2.221

2.017

2.961

2.689

3.701

3.362

45

30

0.737

0.676

1.475

1.351

2.212

2.027

2.949

2.702

3.686

3.378

30

45

0.734

0.679

1.469

1.358

2.203

2.036

2.937

2.715

3.672

3.394

15

43

0.731

0.682

1.463

1.364

2.194

2.046

2.925

2.728

3.657

3.410

47

15

0.728

0.685

1.457

1.370

2.185

2.056

2.913

2.741

3.642

3.426

45

30

0.725

0.688

1.451

1.377

2.176

2.065

2.901

2.753

3.627

3.442

30

45

0.722

0.692

1.445

1.383

2.167

2.075

2.889

2.766

3.612

3.458

15

44

0.719

0.695

1.439

1.389

2.158

2.084

2,877

2.779

3.597

3.473

46

15

0.716

0.698

1.433

1.396

2.149

2.093

2.865

2.791

3.582

3.489

45

30

0.713

0.701

1.427

1.402

2.140

2.103

2.853

2.804

3.566

3.505

30

45

0.710

0.704

1.420

1.408

2.131

2.112

2.841

2.816

3.551

3.520

15

46

0.707

0.707

1.414

1.414

2.121

2.121

2.828

2.828

3.536

3.536

45

o t

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

O f

Bearing.

Distance 1.

Distance 2.

Distance 3.

Distance 4.

Distance 5.

Bearing.

45° -60'

30°-

-45

76

Bearing.

Distance 6.

Distance 7.

Distance 8.

Distance 9.

Distance 10.

Bearing.

O f

Lat

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

O f

30 15

5.183

3023

6.047

3.526

6.911

4.030

7.775

4.534

8.638

5.038

59 45

30

5.170

3.045

6.031

3.553

6.893

4.060

7.755

4.568

8.616

5.075

30

45

5.156

3.068

6.016

3.579

6.875

4.090

7.735

4.602

8.594

5.113

15

31

5.143

3.090

6.000

3.605

6.857

4.120

7.715

4.635

8.572

5.150

59

15

5.129

3.113

5.984

3.631

6.839

4.150

7.694

4.669

8.549

5.188

45

30

5.116

3.135

5.968

3.657

6.821

4.180

7.674

4.702

8.526

5.225

30

45

5.102

3.157

5.952

3.683

6.803

4.210

7.653

4.736

8.504

5.262

15

32

5.0SS

3.180

5.936

3.709

6.784

4.239

7.632

4.769

8.481

5.299

58

15

5.074

3.202

5.920

3.735

6.766

4.269

7.612

4.802

8.^57

5.336

45

30

5.060

3.224

5.904

3.761

6.747

4.298

7.591

4.836

8.434

5.373

30

45

5.046

3.246

5.887

3.787

6.728

4.328

7.569

4.869

8.410

5.410

15

33

5.032

3.268

5.871

3.812

6.709

4.357

7.548

4.902

8.387

5.446

57

15

5.018

3.290

5.854

3.838

6.690

4.386

7.527

4.935

8.363

5.483

45

30

5.003

3.312

5.837

3.864

6.671

4.416

7.505

4.967

8.339

5.519

30

45

4.989

3.333

5.820

3.889

6.652

4.445

7.483

5.000

8.315

5.556

15

34

4.974

3.355

5.803

3.914

6.632

4.474

7.461

5.033

8.290

5.592

56

15

4.960

3.377

5.786

3.940

6.613

4.502

7.439

5.065

8.266

5.628

45

30

4.945

3.398

5.769

3.965

6.593

4.531

7.417

5.098

8.241

5.664

30

45

4.930

3.420

5.752

3.990

6.573

4.560

7.395

5.130

8.217

5.700

15

35

4.915

3.441

5.734

4.015

6.553

4.589

7.372

5.162

8.192

5.736

55

15

4.900

3.463

5.716

4.040

6.533

4.617

7.350

5.194

8.166

5.772

45

30

4.885

3.484

5.699

4.065

6.513

4.646

7.327

5.226

8.141

5.807

30

45

4.869

3.505

5.681

4.090

6.493

4.674

7.304

5.258

8.116

5.843

15

36

4.854

3.527

5.663

4.115

6.472

4.702

7.281

5.290

8.090

5.878

54

15

4.839

3.548

5.645

4.139

6.452

4.730

7.258

5.322

8.064

5.913

45

30

4.823

3.569

5.627.

4.164

6.431

4.759

7.235

5.353

8.039

5.948

30

45

4.803

3.590

5.609

4.188

6.410

4.787

7.211

5.385

8.013

5.983

15

37

4.792

3.611

5.590

4.213

6.389

4.815

7.188

5.416

7.986

6.018

53

15

4 776

3.632

5.572

4.237

6.368

4.842

7.164

5.448

7.960

6.053

45

30

4.760

3.653

5.554

4.261

6.347

4.870

7.140

5.479

7.934

6.088

30

45

4.744

3.673

5.535

4286

6.326

4.898

7.116

5.510

7.907

6.122

15

38

4.728

3 694

5.516

4.310

6304

4.925

7.092

5.541

7.880

6.157

52

15

4.712

3.715

5.497

4.334

6.283

4.953

7.068

5.572

7.853

6.191

45

30

4.696

3.735

5.478

4.358

6.261

4.980

7.043

5.603

7.826

6.225

30

45

4.679

3.756

5.459

4.381

6.239

5.007

7.019

5.633

7.799

6.259

15

39

4.663

3.776

5.440

4.405

6.217

5.035

6.994

5.664

7.772

6.293

51

15

4.646

3.796

5.421

4.429

6.195

5.062

6.970

5.694

7.744

6.327

45

30

4.630

3.816

1401

4.453

6.173

5.089

6.945

5.725

7.716

6.361

30

45

4.613

3.837

5.382

4.476

6.151

5.116

6.920

5.755

7.688

6.394

15

40

4.596

3.857

5.362

4.500

6.128

5.142

6.894

5.785

7.660

6.428

50

15

4.579

3.877

5.343

4.523

6.106

5.169

6.869

5.815

7.632

6.461

45

30

4.562

3.897

5.323

4.546

6.083

5.196

6.844

5.845

7.604

6.495

30

45

4.545

3.917

5.303

4.569

6.061

5.222

6.818

5.875

7.576

6.528

15

41

4.528

3.936

5.283

4.592

6.038

5.248

6.792

5.905

7.547

6.561

49

IS

K511

3.956

5.263

4.615

6.015

5.275

6.767

5.934

7.518

6.594

45

30

4.494

3.976

5.243

4638

5.992

5.301

6.741

5.964

7.490

6.626

30

45

4.476

3.995

5.222

4.661

5.968

5.327

6.715

5.993

7.461

6.659

15

42

4.459

4.015

5.202

4.684

5.945

5.353

6.688

6.022

7.431

6.691

48

15

4.441

4.034

5.182

4.707

5.922

5.379

6.662

6.051

7.402

6.724

45

30

4.424

4.054

5.161

4.729

5.898

5.405

6.635

6.080

7.373

6.756

30

45

4.406

4.073

5.140

4.752

5.875

5.430

6.609

6.109

7.343

6.788

15

43

4.388

4.092

5.119

4.774

5.851

5.456

6.582

6.138

7.314

6.820

47

15

4.370

4.111

5.099

4.796

5.827

5.481

6.555

6.167

7.284

6.852

45

30

4.352

4.130

5.078

4.818

5.803

5.507

6.528

6.195

7.254

6.884

30

45

4.334

4.149

5.057

4.841

5.779

5.532

6.501

6.224

7.224

6.915

15

44

4.316

4.168

5.035

4.863

5.755

5.557

6.474

6.252

7.193

6.947

46

15

4.298

4.187

5.014

4.885

5.730

5.582

6.447

6.280

7.163

6.978

45

30

4.280

4.206

4.993

4.906

5.706

5.607

6.419

6.308

7.133

7.009

30

45

4.261

4.224

4.971

4.928

5.681

5.632

6.392

6.336

7.102

7.040

15

45

4.243

4.243

4.950

4.950

5.657

5.657

6.364

6.364

7.071

7.071

45

o t

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

Dep.

Lat.

O f

Bearing.

Distance 6.

Distance 7.

Distance 8.

Distance 9.

Distance 10.

Bearing.

45° -.60:=

A TABLE OF THE ANGLES

Which every Point and Quarter Point of the Compass makes with the Meridian.

North.

Points.

0-iA

1 II

2 48 45

5 37 30

8 26 15

11 15

Points.

O-V4

0-8|

South.

N. by E.

N. by "W.

S. by E.

S. by "W.

N.N.E.

N.N.W.

1-%

14 3 45
16 52 30
19 41 15
22 30

1-14

S.S.E.

S.S.W.

N.E. by N.

N.-W. by N.

2->A

25 18 45
28 7 30
30 56 15
33 45

2-iA

2-»i
3

S.E. by S.

S.W. by S.

N.E.

N.W.

3-%

36 33 45
39 22 30
42 11 15
45

3-%

S.E.

S."W.

N.E. by E

N.W.byW.

4-V*

i-Vt

4-%
5

47 48 45
50 37 30
53 26 15
56 15

1:|

5 *

S.E. by E.

S.W. by W.

E.N.E.

W.N.'W.

59 3 45
61 52 80
64 41 15
67 30

5-V,

E.S.E.

W.S.W.

E. by N.

W. by N.

70 18 45
73 7 30
75 56 15
78 45

7

E. by S.

W. by S.

East.

"West.

7-%

81 33 46
84 22 30
87 11 15
90

East.

West.

'^^ FOR REFERENCE

Vl'ft

NOT TO BE TAKEN FROM THE ROOM

BW CAT. NO. 23 012 »*!'J«4

UC SOUTHERN REGIONAL LIBRARY FACILITY

A A 000 084 216 1